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Inherent Gift: along the lines of Piers Anthony's Xanth books, in which characters are born with abilities that are quite specifically defined, in addition to their superhuman ability to survive puns. This also can happen in Magic Realism. Often the Inherent Gift is simply the ability to use magic, in which case it's often hereditary. If it's not general magic, it's usually elemental powers.
Theurgy: where the magic is done entirely by spirits, gods and cosmic entities with whom the caster makes deals; the "caster" in this case knows nothing more than a glorified phone number — and preferably how to negotiate really well. The fictionalized version of "Wiccan" magic seen in Buffy the Vampire Slayer and, to a lesser extent, Charmed is mostly Theurgy. The clerics of Dungeons & Dragons and the Priests of World of Warcraft both practice Theurgy (as does any real-world religion whose deity or deities are said to answer prayers of the faithful with miracles and/or intercessions). When Magic itself is a kind of entity with which casters make bargains and cut deals, this becomes a variety of Wild Magic (below). Modern conceptions of necromancy are generally portrayed as this, or Rule Magic with this in varying amounts.
Rule Magic: where some underlying magical rule system is applied, as in manipulation by "True Name" or sympathetic symbolism, or elaborate ritual. Most "study spells and say words of power" magic seen in fantasy literature, films and TV shows are Rule Magic. Real world examples include Wicca, Hermeticism, Kabbalah, and Onmyodo. Vancian Magic is a completely fictional example. This variety is where you find things like the "Law of Contagion" — that is, if you have a piece of the target, you can affect it from afar since it's still part of a "whole", even if it's miles or kilometers distant. This is, however, usually just one rule in a larger system. This form is heavily dependent on The Laws of Magic or the author's own custom-made limitations.
Alchemy: Magical chemistry. Effectively a variety of Rule Magic, but it is limited to creating magical substances rather than the direct application of power/energy by force of will. Differs from other Rule Magics in that it often employs only the magic inherent in the materials used, rather than magic from the "caster"; depending on the setting, practitioners of alchemy may or may not have (or be required to have) magical ability of their own.
Wild Magic: No one has any control over what happens or when it happens, although sometimes these can be influenced. The magic is basically alive. It has its own will and its own agenda or, more often, its own set of rapidly changing whims no sane person could hope to predict and it will only help you if it feels like it. Finagle's Law often applies. Usually Magic Realism permits only this and Inherent Gift.
In many settings, whatever sort of magic is present, not everyone can work it, or some people can work it much better than others — so any of the other types can overlap with Inherent Gift magic. If such a gift only works, or works much better, if the gifted individual is properly trained, that's Training The Gift Of Magic.
While some magical systems allow it to do practically anything, restricted only by the user's power and imagination, in other systems the magic user is restricted to variations on a theme. Classic styles are:
Transmutation: Transforming something into something else. Likely to involve Equivalent Exchange, as noted below (you can't turn nothing into something). Most forms of alchemy involve transmutation, as seen in the classical 'turning lead into gold' trick. At its most extreme, this form of magic may also involve Shapeshifting (either of the caster or of someone else), when it's not an innate ability of the caster's race.
Equivalent Exchange: This is when a spell or magical effect requires a sacrifice of equal value to work. This is often a feature of alchemical, theurgic or wild magic systems, where the books must be balanced for every magical effect performed.
Mentalism: Power over the minds and emotions of others. Quite often involves Mind Control and abilities that mimic Psychic Powers in a magical context.
Blood Magic: Usually stereotyped as the blackest of Black Magic, this is magic fueled directly by the shedding or spilling of blood, usually in the form of human or animal sacrifices. The blood mage draws on the energies of death and dying, or gains access to whatever magical energies the sacrifice possessed, or both, and uses them either to cast spells (which are almost always themselves rather unpleasant) or increase his personal power level. Blood Magic can also have a White side, though, where voluntary or personal sacrifice produces powerful effects out of proportion to the apparent magical cost involved, or which are impossible to overcome with darker magics.
These styles of magic crosscut the list of ways of doing magic above. While divining is often an inherent gift, there are also examples of pure diviners, unable to do any other style of magic, who see the future through theurgy, rule magic, device magic, or wild magic (or a combination). Whatevermancy is a common naming convention for fantasy magical styles. See Magic A Is Magic A. With all this wonderful diversity, you can expect some snobbish magicians to consider there are Un Equal Rites. If practicing magic has a spiritual component, it may cross over with Enlightenment Superpowers. This Wiki has an article on writing Functional Magic systems.
See also Our Mages Are Different; this trope is Our Magic Is Different.
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Anime and Manga
Alchemy, naturally, is the Functional Magic of Fullmetal Alchemist. Exceptionally talented alchemists are close to, but not quite, Rule Magic users, the only hard-and-fast rule being Equivalent Exchange. Still, "Equivalent Exchange" is only used partially, as alchemists seem to need to worry about balance only when matter is involved, but there's a considerable amount of energy that seems to come from nowhere (even if one were to use matter as the energy source, you'd still need a lot of energy to make fission alone, and a lot more energy just to convert the resulting energy into the into the adequate form of energy).
It's outright stated in the series that the energy for alchemical reactions is drawn from tectonic shifts. There are two anime and a manga, with a total of.. three power sources: Tectonic shifts, at least for alkhahestry; The suffering of -our- world; another is the souls from Father, being pumped into Amestris.
It's Amestrian Alchemy that uses the movement of the tectonic plates (Father is suppressing it somewhat, and totally later on), alkahestry uses "the dragon's pulse" which seems to be something along the idea of Ley Lines and the third is the philosopher's stone condensed human souls. Those three are from the manga and Brotherhood, the first anime had only one: human souls, albeit from two places. Condensed into a philosopher's stone in that world, but all other alchemy was powered by souls from another( our) world.
Bleach: Kidou is a form of Rule Magic that can be used offensively, defensively, and also for healing, tracking and long-distance communication. In the hands of a skilled practitioner and at high enough levels, it can even manipulate space and time. The main requirement for being able to use even basic levels of kidou is the possession of spirit power but shinigami can only excel at kidou if their spiritual strength is great enough. Kidou is taught via incantation that requires a spellcasting chant as well as specifying the classification, level and individual name of the spell. With increasing levels of skill and talent, kidou users can skip chants, double-chantnote cast two spells at the same time, hide spells within other spellsnote which can even be done in multiple layers. At one point Urahara hides a spell inside a spell that's hidden inside yet another spell... and distracts the target first by casting a chain of half a dozen other spells, and even delay verbalising the classification/level/name part of the spell until after the spell has been castnote very useful for emergency barriers that need to be activated swiftly in combat. There are even some hints that one or two very high-level kidou users can cast kidou entirely non-verbally. The catch is that the less verbalisation involved in the casting, the weaker the spell actually is when released. This means it doesn't just require technical skill to start discarding the verbal component, it also requires great spiritual strength to be able to pull off weakened spells that are still strong enough to do their jobs.
One Espada (Zommari) has displayed a technique called Amor which was considered the equivalent to kidou. It was more akin to the "Inherent Gift" style of Functional Magic and was unique to Zommari rather than being something any, or even most, hollows can develop.
There have been occasional references throughout the manga to the Quincies possessing some techniques that are equivalent to kidou and which behave in a rule magic manner but focused through a device that acts as some kind of focus. However, this hasn't yet been explored in as in-depth a manner as kidou.
The Slayers uses all of the above listed types at some point. Most humans are restricted to Theurgy and Rule Magic with a bit of Alchemy thrown in for good measure. The Mazoku and Dragons use a combination of Inherent Gifts and Rule Magic. A lot of the Theurgy in this setting calls upon the really powerful Mazoku. Wild Magic shows up when Lina finds out that Giga Slave has the capability of actually summoning the Lord of Nightmares, Chaos herself, into the world, and if the casting is performed incorrectly, allows Chaos free rein to do anything she likes.
In keeping with its origins in Dungeons & Dragons, various forms of Functional Magic appear in Record of Lodoss War. Sorcerers use Rule Magic, priests use Theurgy, and elves use both Theurgy and Inherent Gifts. Device Magic in the form of magic swords, wands, and artifacts abounds.
Scrapped Princess appears to use a form of theurgy, except the gods that are invoked are unthinking machines that follow commands without judgment.
Getter Robo's "Getter Rays" are initially thought to be a new and versatile form of radiation, but this is only partially true. Later on in the continuity, they are revealed to be alive, intelligent, inscrutable, and by most definitions supernatural. Therefore using them could be considered a kind of theurgy or wild magic, the rays will only let you do stuff that it agrees with. As this show is a classic Super Robot series, this gives a justification for The Power of Friendship and raw idealism being used to win battles. In later iterations of the series, the rays shift from rewarding friendship and hope to responding to (and sometimes creating) sheer berserk rage.
Naruto is a mix of Theurgy, Rule Magic, and Inherent Gift. While most of the techniques fall under Rule Magic (as they have to be studied, learned and shaped to perform them), the Inherent Gifts (the various Bloodline Limits such as Byakugan and Sharingan) play a part too. The Theurgy comes into play in that the Summoning technique requires the summoner to sign a contract with the creature they're summoning.
Beyblade is an odd combo of Theurgy, Device Magic, and Wild Magic. OK, it's mainly Device Magic, as most of their power comes from odd creatures inhabiting their magic tops. But they have some sort of deal with these creatures (Theurgy). Also, if you're not battling with your whole heart, or if you tick off your creature, it can up and leave you (Wild Magic).
Similarly, when real magic is used in Yu-Gi-Oh! and Yu-Gi-Oh! GX, it's a mixure of Theurgy, Device Magic, and Wild Magic. The Millennium Items of the first show and Shadow Charms of the second show are perfect examples of Device Magic (with a bit of Theurgy thrown in, in the form of ritual sacrifices and pact with whatever spirit is trapped in them), while the Duel Monsters themselves are the embodiment of Wild Magic (with the same Theurgy requirement to use their powers for real as the Items/Charms).
Nen powers in Hunter × Hunter seem to be a mix of Inherent Gifts and Rule Magic: there are specific ways of using Nen, but each Nen user tends to specialize in and develop a specific ability based on one of the six forms of hatsu (specialized Nen usage): enhancement, emission, manipulation, conjuration, transmutation, and specialization. Furthermore, one can impose limits on their own powers in order to enhance them. Another way of looking at Nen (literally: Mind Force) is a mixture of aura and will. Thus, Nen is essentially a physical manifestation of one’s will which is why there are ultimately no boundaries to the possible forms that it can take (imagination being the only limiting factor in that regard). Subsequently, Nen powers are affected by their user’s mental state and might not work properly if he or she is scared, undetermined and so on.
While Belldandy of Ah! My Goddess does have her own supernatural abilities, most of her magic is Theurgy bordering on animism — she casts spells by speaking to the spirits inhabiting objects. She actually describes herself as being like a telephone line at one point, and was originally summoned though a mis-dialed (or deifically redirected) telephone call.
Mahou Sensei Negima! uses nearly every single magic style listed here, most likely because Ken Akamatsu is such an RPG fan. The largest magical source is Force Magic, as was once explained as magic being an ingrained part of all things, and that mages learn to harness this in creating or chanting spells, tying in with Rule Magic — mages usually use spells by chanting a magic release key and an often string of words, in Latin or some other ancient tongue. They sometimes use a catalyst for their spells. The abilities of the user can grow depending on the proximity to certain Places Of Power. They also used this with the Inherent Gift variety in that magic is also ingrained in the people who use it, meaning that at least half of all magic spells are based on the spell-caster's abilities. Theurgy is also used, in that the more sentient effects of magic (such as spells remaining active while the mage takes his mind off of it, or projectile spells continuing to fly after use) are explained as the work of ancient spirits watching over or advising the actions of living mages (making the series premise seem like less of a Contrived Coincidence). Finally, a mage's power can also be strengthened by holding or using certain powerful Devices, or some powerful spells can be represented by certain objects, such as the Pactio cards. Surprisingly, Akamatsu hasn't used elemental-style magic as strongly as most other magic series.
The Stands of JoJo's Bizarre Adventure combine many forms of magic together. It is predominantly a combination of Theurgy and Summon Magic, where Stands are materialized forms of their users' spirits and psyches. It also incorporates Rule Magic, as there are rules that all Stands follow, the most prominent being 1) People are limited to one Stand each, although a Stand can evolve into a more powerful form in certain conditions (Star Platinum, Echoes, Whitesnake and its evolutions, Tusk); 2) any damage incurred by a Stand is shared with its user, and vice versa (if a Stand loses a limb, the user will also lose the respective limb, and vice versa); and 3) Stands are Invisible to Normals: only those with a Stand can see other Stands (unless the Stand is bound to a physical object) and appear as psychic phenomena to normals. The individual capabilities of Stands draw upon other forms of Functional Magic: Magician's Red uses Elemental Magic, specifically fire; Hermit Purple can use Divination in the form of psychography with cameras and televisions; Ebony Devil combines Device Magic with Black Magic, being bound to a doll and gaining power the more its user is injured; and Gold Experience can use Transmutation to turn objects into living creatures, just to name some examples. Stands also incorporate elements of Inherent Gift: many people are born naturally with Stands, while others can only acquire Stands by using the Bow and Arrow.
The precursor to Stands, "Hamon" (or "Ripple"), is a form of Force Magic and Rule Magic where the user harnesses their own innate life-force via special breathing techniques and convert it into other forms of energy, typically sunlight, the weakness of vampires, zombies, and Pillar Men. The applications of Hamon are incredibly varied, as demonstrated prominently in Part 2 by Joseph. The main weakness of Hamon is that it is reliant on proper breathing: if anything hampers breathing or the transmission of oxygen through the body, like blood loss, extreme cold, or good old fashion choking, then the user's Hamon weakens and eventually becomes inert.
Lyrical Nanoha uses Inherent Rule Magic with Devices. A person has to be born with the ability to use magic, but to be an effective mage, one needs to study up on the mathematical formulas that makes up the various spells (Nanoha and Fate, two of the strongest mages in the series, are both math geniuses as well). And of course, there are the various Intelligent, Armed, and Storage Devices in the series that helps a mage process said spells.
Shaman King uses a Theurgy and Inherent Gift style way of summoning; most people can't see spirits, but some are naturally born with the ability to see them (Shamans). The Shaman can then make a deal with a spirit to act as a partner to them.
Spiral energy from Tengen Toppa Gurren Lagann is capable of freely manipulating the laws of physics when enough is present. It appears at first to be Device Magic (since no one was seen using it outside a Ganmen) but is actually Inherent Gift/Force Magic: every living being capable of evolution can produce it. Channeling is done through the user's fighting spirit which humanoid beings are naturally better at. The only viable tactic against Spiral-wielders is to demoralize them into despair. One more caveat is the Spiral Nemesis: while it can warp reality, Spiral energy can and will collapse the entire universe into a black hole if overused.
Fairy Tail uses quite a lot of these, being a series that centers around mages. Theurgy exists through the main character's use of Summon Magic, many have elemental magic, Charle and her mother have powers of divination, Mirajane and her siblings have powers of transmutation on themselves, Mest has the power of mentalism to alter memories, a few side characters use Magic Music and nature magic, and Black Magic exists, almost always used by the villains.
The main theory in magic is "Idol Theory", a form of The Law of Contagion and thus a form of Rule Magic where an "idol" or a duplicate of a holy object receives power from the actual object. That is, if one were to make a duplicate of the cross on which Christ died, the duplicate will receive power from the actual cross, although it's a very small fraction, similar to how the Sun provides energy to solar panels, but the solar panels cannot reach the same amount of energy that the actual Sun provides.
Due to Idol Theory, Device Magic is employed to make use of it.
Force Magic is alluded to occasionally; Volume 14 has mentions of ley lines, and mana and telesma are mentioned as sources of magic power.
Index uses Magic Music and mental codes to cast spells.
God's Right Seat uses a limited form of Theurgy combined with the Idol Theory above — each of them has a particular angel from which they draw their powers from, and a special ability derived from a certain aspect of God.
Soul Eater uses both Inherent Gift (with the witches) and Device Magic (with the Demon Tools).
Kubera's system relies on incantations combined with mathematical calculations, which we can see during the flashbacks where Asha and Brilith are taking their magician certification exams. Magic is actually borrowed from the gods and a human's divine affinity determines how much they can accomplish with their spells. The alternative non-human system of transcendentals relies upon a user's own power and seems to be more limited in scope, with many transcendentals being unique to each user.
The Grid isn't the only place-as-device in device magic. The Speed Force (a Force Magic) powers all DC Comics speedsters, regardless of their individual origins (which are deemed, in current continuity, to have given them not speed itself, but access to the Speed Force.)
A device that is both place and item is the Marvel Universe's M'Kraan crystal, though failed attempts to harness it can have extremely disastrous results for all of reality (perhaps making it a form of Rule Magic, which can become unpredictable when the 'rules' aren't followed.)
Most comic book universes are a Fantasy Kitchen Sink with all kinds of magic, but a mix of Force Magic and incantation-based Theurgy ("By the Hoary Hosts of Hoggoth!") are common for comic book magic users. Device Magic, in the form of an Artifact of DoomMacGuffin, are frequent plot devices.
Marvel Comics' Doctor Strange, whose explicit title is "Master of the Mystic Arts," uses all of the above, including blood and sacrifice magic if necessary. (He doesn't like to do it, but he'll still do it).
There is a lot of time spent discussing how everything works through the First Circle (Natural reality and the art of causing excessively improbable things to happen through Chi), the Second Circle (Impossible things that have precedent, willed into being through Magic), the Third Circle (Concepts forcing themselves to be and always have been at the expense of gaining Paradox). Each Circle is very vulnerable one to the one 'above' it.
Aaron wrote a lot about how he believed chi worked across various manga and it appears that the new world he's arrived in follows his Five Chakra system exactly, even though the local expert, Doctor Tofu, has only discovered part of how it works and how it can be used to boost abilities.
Wind Chakra – temple – intellect, speed and agility.
Water Chakra – sternum - health and vitality.
Earth Chakra - stomach - stamina and resistance.
Fire Chakra – crotch – passion and strength.
Void Chakra – the aura outside the body – perception.
Madonna, Principle of Motherhood and mother of Discord, displays a Rules Magic variety. She is unable to use her magic for herself. She can only use it for the direct good of her children, like making a cup of unlimited chocolate milk for Discord.
Inherent Gift—very rare (all the in-book examples are from outside the universe).
New Zork is almost nothing but Inherent Gift, except for a couple of spells, like silence, that are “commercially available.”
Alchemy. “God bless healing potions!”
Force Magic—the wizards of C'hou tap into the kvar, or Field, the raw magic that surrounds everything; they weave it through their bodies and any “spellfuel,” then release it to do whatever. They don't always succeed, either. Paul has learned three spells this way.
Device Magic, ranging from household magic (e.g., glowstones) to useful adventurers' things like self-propelled boats to legendary relics like the Kansael.
The Hunter relies exclusively on Device Magic, but there are other forms in his world.
Child Of The Storm: The most prevalent kind is Inherent Gift, but you have Device Magic in the form of Mjolnir, the Darkhold and the Green Lantern Ring. Force Magic and Theurgy are mentioned, with, apparently, Magic being a fundamental force of the universe, and there's an all encompassing element of Wild Magic, with many characters noting that magic is just a tiny bit alive.
Of the sub schools, Elemental appears when Loki manipulates water and it turns out that Harry favours fire (bothofthem). Necromancy appears more often than anyone would like.
The Force in the Star Wars universe is, of course, an example of Force Magic. Considering that Jedi are basically clergy with light sabers, there's an element of Theurgy as well.
Peter S. Beagle's The Last Unicorn uses Rule Magic for wizards and witches and Inherent Gifts for magical beings such as the titular unicorn. Magic sometimes act like Wild Magic for Schmendrick the Magician, but this is because he is incompetent. He has an intuitive grasp of magic that comes to him in moments of great emotion; but even then, he speaks certain words in a certain way to use it.
Zig-Zagged in Terry Brooks' Shannara series — the magic of the series is constantly changing and evolving, so at its heart it's Wild Magic, except that it will (seemingly of its own accord) settle down and act like one of the other types (typically Rule Magic and/or Inherent Gift) for centuries at a time. It's tricky that way.
The Tortall Universe books, especially the latter series that focus heavily on expanding the setting, have lots of this. To explain in detail would be a page of its own, but magic can be used for everything from instantaneously cleaning an outfit, to tracking someone down, and turning mere stones into glowing, fully functional lanterns.
In The Witcher series, both novel and games, magic is a mix of Rule Magic, Force Magic, and Innate Gift. All magic derives from Chaos. Unlike many other settings, Chaos is non-native to the universe of the Witcher series, instead originating from a dimensional cataclysm in the distant past. A user of magic or object with a great deal of power is called a Source. Some children are born as Sources, and must be trained, or their abilities will eventually drive them mad. Spellcasting itself is extremely complex, taking years of study, requiring detailed knowledge of the sort of magical feat you are trying to perform, such as detailed biology notes for shapechanging, detailed coordinates for teleportation. This means Sorcerers and Sorceresses are extremely well-educated, comparable to modern-day scientists, making them valuable advisors to Kings. Witchers use heavily simplified single-effect spells called Signs which do one thing and one thing only, usually things useful to aiding their primary profession of hunting monsters.
In an amusing subversion on the stereotype of the Hot Witch that comes up often in fiction, the novels note that anyone willing to give up a daughter to mages to be trained generally didn't have much use for the girl, as a trained sorceress would have bigger concerns then her birth family once fully trained: if they were pretty they would be married to cement political allegiances or broaden the family to help out farmers or family business. Therefore, most sorceresses started out as the kind of girls nobody would want to marry, namely rather homely ones. They only become beautiful after they're trained with magic and have their bodies altered to look better, because sorceresses are expected to be attractive-looking. This often causes them to have a slight chip on the shoulder towards women who were naturally born beautiful, leading to the Vain Sorceress stereotype seen in fairy tales.
Steven Brust's Dragaera series has four different kinds of Force Magic:
Sorcery, where the force comes from raw chaos filtered through the Imperial Orb.
Pre-empire sorcery, where the force comes directly from raw chaos.
Witchcraft, where the force is the caster's own psychic energy manipulated by rituals.
Psychics, where the force is the caster's own psychic energy manipulated directly by the mind.
Inherent Gift: Everyone has some spark of magic in them and can manipulate magic - in Backup Thomas says anyone can learn it to some degree or another, comparing his own skills to Harry's as taking a six-month correspondence course to having Ph.Ds from three separate Ivy League schools. There is also some measure of hereditary talent passed on matrilineally. However, if the talent is outright rejected by the time you reach a certain point in your life you lose it altogether, and you lose the ability to pass it on to your descendants. Molly Carpenter narrowly avoided this deadline; her mother rejected her magical talent because she's a deeply religious woman, and, well, the Bible does say a bunch of nasty stuff about witches, which is discussed in a later book)
Theurgy: Various demons, faeries, and other things have been summoned. This is generally a bad idea because they are rarely happy about it. There are also rites, described as a magical vending machine. Mess up a rite and the sponsor being gets upset.
Rule Magic/Force Magic: Most spells are a weird combination of all three. Magic is described as more of a power source that wizards tap into, magic words are just to help them control it. Use words that are too familiar to you, use magic without proper concentration, or just plain screw up and it can go bonkers. Meaning it does everything from not working, to random explosions, to giving you a seizure. Familiarity is a problem because magic is all about what you believe and think in the Dresdenverse. Associate giant balls of napalm too closely with the word "fire" and you have problems of the insurance variety.
Alchemy: All potions are made with 7 ingredients (one for each sense, one for the mind, and one for the soul) plus a liquid base. What the ingredients are varies between potions and wizards, and are mostly symbolic.
Device Magic: Wizards can enchant items, using one of two methods. Either cheap, short term enchantments that need recharging or more expensive permanent enchantments. Apparently misuse or improper enchanting can lead to anyone using the object getting seriously surprised.
Divination: Future sight does happen, but it's generally too vague to help before it's immediately useful. Some wizards have a short-ranged future sight, often to about three seconds, though they see what's likely to happen, not a deterministic path. Doing divination outright violates one of the Laws of Magic, and as such is grounds for summary execution.
There is a specific attribute of certain being called "Intellectus" which is seemingly a form of limited omniscience. They don't know everything all the time, however they will know the answer to any question through virtue of asking it. Harry compares to a normal person who would have to go through the process of solving a quadratic equation, whereas a being with Intellectus would just look at the problem and know the answer without having to actually go through the process of solving it. It is also mentioned that beings who have this ability are ridiculously old and powerful.
Elemental Magic: Most wizards specialize in a certain area of magic. Harry prefers fire and force spells for example. Harry used to use wind magic a lot but rarely does so anymore, since he got better with force magic.
Necromancy: Generally frowned upon, but not inherently evil. Using human corpses is evil, because it allows a wizard control over another person, a big no-no in the Dresdenverse. The line of reasoning is that you think along the lines of what you do, and when what you do is enslave dead people to your will, you aren't thinking happy thoughts.
There are also Ectomancers, people capable of speaking to ghosts.
White Magic: What all "normal" magic is called. Also means legal magic.
Black Magic: Two things get called black magic. One is normal magic tainted by being used in evil ways (to kill other people, mind-control them, etc.). The other is a special power source, described as nauseating and vile, used by vampires (Red and Black Court, at least) and those wizards who have tapped into Kemmler's form of necromancy — pretty much the ultimate in The Dark Arts in the setting.
Equivalent Exchange: Basis of a spell's power. A wizard can either use their own energy, stored energy in an enchanted object, or the ambient energy around them (Harry once froze water by sucking the energy from it).
Magic in The Lord of the Rings is inherent to elves and wizards, although wizards also focus their inherent power through a staff or use device magic for certain effects. Other tricks they use, such as summoning animals, are exercises of lore. Sauron used device magic when he channelled his inherent power into rings.
Force Magic is also brought up in the background lore. It's explained that whenever Arda was created, magic was woven into the fabric of creation.
We have Magic Music as well; Eru Ilúvatar created the world through song, and the Valar helped create the world with music. The elves themselves sometimes employ magical music.
Magic in C. S. Lewis's The Chronicles of Narnia is usually rule magic using words, gestures, and other symbols, although some devices exist, such as Susan's horn and Jadis' wand. Hints of necromancy exist. Divination is practiced — most often by centaurs. One witch also uses mentalism, magic music, and shape-shifting. The character Aslan uses an inherent gift to create almost any effect he desires since he's actually Lewis' allegory for God the Son. However Aslan states that he has limitations with his magic, but these limitations are self-imposed. He says he "follows his own rules." Aslan himself also used song in order to create Narnia.
Jadis' species (said to be a cross between giants and Jinn) also possess an Inherent Gift. Jadis also states that in the world of Charn, Rule Magic was outlawed and only those with Inherent Gifts were allowed to practice magic.
Orson Scott Card's The Tales of Alvin Maker series is set in an alternate America full of Functional Magic, where whites have Inherent Gifts, Africans have Device Magic and Native Americans have Force Magic. These distinctions are cultural, not racial, and it is possible (albeit very difficult, especially as one gets older and more set in one's cultural identity) to learn another culture's form of magic.
A subtle form of device magic appears in Angela Carter's Nights at the Circus. Sophie's foster mother Lizzie is a witch who can control the flow of time with the help of an antique clock. The clock is eventually destroyed in a train accident, and time slips out of her control.
Rick Cook's Wiz Biz series of novels have the magical races (elves, dragons) possess Inherent Magic, while the humans use Rule Magic with a dash of Theurgy. Wiz further codifies the Rule Magic: where previously a human must study for years the exact words and actions to perform a spell, Wiz uses the inherent rules behind the Rule Magic to create a programming compiler for such.
The Chronicles of Thomas Covenant by Stephen Donaldson uses Rule, Force, Device, and Wild Magic. In an odd subversion, the most commonly used rule magic, called "Earthpower," is actually a conscious wild magic that voluntarily submits to control by words and devices, whereas what is called "wild magic" in the book is actually force magic released from matter and controlled by the mind of the one wielding the white gold.
In Diane Duane's Young Wizards series, magic is a combination of Rule Magic and plain old cajoling. Essentially magic is a way to talk to things (whether alive or not) and convince them to change the way they are or the way they act, using a special Speech. However, actual spells require intensely specific magic circles and incantations to work properly, to the point where magic and magical research begins to highly resemble writing computer programs. The wizards in question are quite literally the tech support staff of the universe, which is a deliberately created artifact, so this is to be expected. Still, as one character puts it, "The powers knew how it worked when it was fresh from the factory. We know how to handle all the little quirks it's developed since." A sufficiently complex system will develop quirks that seem like wild magic to the uninitiated. This is true today, it would be a thousand times truer for a full universe.
David Eddings' The Belgariad uses several different types. The primary one is sorcery, which tends to defy description (Inherent Gift comes close, though), since the practitioner can basically do nearly anything (subject to personal power). Other examples include Theurgy (witchcraft and magic, which involve summoning and cajoling/controlling nature spirits and demons, respectively) and apparently Rule Magic (wizardry).
Belgarath explains in the follow-up series The Malloreon that there are several different ways of 'tampering with the nature of things', although his comments on Morindim magic in Belgarath the Sorcerer give the impression that it's just a form of (extremely dangerous) sorcery wrapped up in nonsensical rituals which are only necessary because the magicians believe they are. Perhaps they never figure that out because the average lifespan of a Morindim magician is short, usually ended by being eaten by a demon they lost control of, or another magician's demon.
Magicians are 'sublime egomaniacs who view the very existence of other magicians as a mortal insult', so they're not big on cooperating or sharing knowledge.
The author's The Elenium and Tamuli take place in a world where spells are a form of Theurgy. The incantations are in fact specially-worded prayers to a specific patron deity. If the deity is amenable to the request, they use their power to carry out the wish. The deity themselves receives power from the belief of their followers.
Teresa Edgerton's Celydonn contains different types. Even people who are considered learning disabled in-story (see The Castle of the Silver Wheel) are expected to know the difference between witchcraft and wizardry, so it is never explained by any Mr. Exposition.
Witchcraft is explicitly stated to be the result of an inherent gift for harnessing Wild Magic, which also appears to be Force Magic. In all three volumes of the Celydonn trilogy, it is stated (in varying degrees of detail) that both men and women can possess a talent for witchcraft. In women, the inherent gift usually manifests in early childhood, and in places like Mochdreff, where witchcraft is accepted, it is then subjected to training. In men, the inherent gift is usually latent unless some shock sets it off, when it manifests full-blown (and is often associated with mental instability).
The science of wizardry is Rule Magic. From the conversation between Lord Cado and Gwenlliant in The Castle of the Silver Wheel, it appears that anyone can study it without necessarily possessing an inherent gift.
Note that one may be both a witch (or warlock) and a wizard. All Adepts are both.
Raymond E. Feist's Riftwar Cycle uses almost every variety of magic above, but most of it qualifies as Rule Magic. Even then, there's an Inherent Gift needed, which leads down either the so-called Lesser Path (Device Magic and Alchemy) or Greater Path (Force Magic). It's extremely rare for any magician to be capable, let alone skilled, in both. Beyond that, magicians usually have a talent for one application in particular, such as Pug's mastery of rifts and Miranda being able to effortlessly teleport anywhere she's ever been. Priests also perform a combination of Rule and Theurgy magic, but it hasn't been explored yet whether any talent is needed, or if it's entirely the blessing of the gods. Then there are characters like Nakor and his seemingly random assortment of "tricks," and William's unheard-of natural ability to communicate with animals that fall outside the system altogether. We later find out (from Pug's musings) that all magic is the same magic, and the classifications are completely self-imposed.
The superpowered bards are the most powerful magic-workers. It's a combination of Inherent Gift, Magic Music and rule magic (training to know what you're doing). There's also an element of Wild Magic — any good song played by a Spellsinger will have an effect, but without years of training, the caster doesn't know what that effect will be, although it's implied that the genre and subject of the song always have something to do with it.
There are other magic-users in that series too. Wizards like Clothahump use Rule Magic: Transmutation and Alchemy primarily, with a little Summoning, healing effects, and Divination thrown in. Rune-casters use Divination to locate things or determine the best course of action; Colin could also predict the future, but is possibly unique in that ability. Finally, extreme mental states such as insanity or dying can let magic-users achieve feats far beyond their usual limits.
Esther Friesner's Majyk by Accident series differentiates Magic (stage illusion) from Majyk (a pseudo-living force that puts the spunk into spells, the kick into cantrips, etc). Magique is a third tool but it's just Majyk from concentrate with lots of preservatives and has a tendency to make with the boomcrashtinkletinkle. The series also differentiates the Majyk used by humans (or cats) as opposed to the Majyk ingrained in species like fairies, Welfies (this 'verse's version of elves), or gods.
Magic in Terry Goodkind's Sword of Truth can be used to do anything and thus falls into the category of Force Magic, at least in theory. In reality, most of the magic users stick to established uses for their abilities (light webs, wizard's fire, etc). Everybody except Richard uses Additive Magic although Subtractive Magic is not unheard of. Device Magic is also fairly common.
The above is absolutely the perspective one would naturally come away from "Wizards First Rule" with, but later books in the series go much further in depth regarding the inner workings of the world's magic.
The abilities of most magic users are Inherent Gifts; Richard and the other students at the magic school are referred to as "gifted," and when such abilities awaken in them, they are tracked by magical nuns who bring them back to the magic school to have their abilities refined. Further, many people with specific magical talents are also by birth, such as Confessors and Dreamwalkers.
Magic is explained at length, repeatedly, to be the creation of ruling spirits in the world, the Creator and the Keeper of the underworld, and some magical effects and abilities, such as the increasing prevalence of Subtractive Magic users, are imbued through interaction with agents of these deities.
Still later in the series, other characters attempt to explain that magic is extremely limited in what it can and can't do, defining it as Rule Magic, only for Richard to ignore them and prove that it really is Force Magic after all.
In Barbara Hambly's Darwath books, and her Ferryth books, mages possess an inherent gift, which must then be developed with training in Rule Magic.
Robert Jordan's Wheel of Time books use Force Magic interlaced with Rule Magic, where channelers tap into and draw power from the "True Source" that drives the titular wheel. Channelers are limited in capability to their own personal strength and sex (men and women use different halves of the Source). The series also contains Device Magic ("ter'angreal," which can occasionally be used by non-channelers) and Theurgy (the True Power, which involves drawing power from the Dark One). While channelers draw on a form of Force Magic, it is used exclusively as Geometric Magic — channelers "weave" different strands of the One Power into patterns which do certain things. Because men and women use different halves of the Source they each have different weaves which do the same thing. It's also stated that when a person learns to do something a certain way (e.g., lighting a candle with a weave of fire) they find it extremely difficult to impossible to learn any other way to do it. There are also several other, less common, forms of magic unrelated to the One or True Powers:
Dreamwalkers can enter Tel'aran'rhiod (essentially a spirit/shadow world that most people only pop in and out of when they dream involuntarily) and manipulate it for a variety of effects, including spying on the real world, entering the dreams of others, and predicting the future. There's some overlap with the One Power - several channelers are shown using the One Power to enter the world of dreams even if they don't possess the inherent ability required - but dreamwalking itself does not require the One Power and there are dreamwalkers who cannot channel.
Wolfbrothers have a spiritual bond with wolves, which lets them communicate with them telepathically, enhance their senses, and enter Tel'aran'rhiod, which also functions as the wolf afterlife (though Wolfbrothers don't have the full range of dreamwalker abilities- they can manipulate the dream environment but not enter human dreams, for example). Wolfbrothers can be at least as capable within the World of Dreams as other dreamwalkers - Perrin is able to stop balefire, something nobody else seems to have even considered the possibility of. Being a Wolfbrother is an inherent gift.
Min has an odd form of divination that lets her sometimes see images around people which predict their futures. Sometimes she knows exactly what it means, and sometimes she has to guess, but no vision she did understand has ever failed to come to pass. She's the only person in the series to show this ability, and Word of God is that while not unique, it's very rare. It is also completely involuntary and, given the nature of events in the series, often shows her bad news.
Hurin, a minor supporting character, has the inherent gift of being able to "smell" violence. This ability is uncommon, but not unheard of.
Recurring villain Padan Fain has a number of bizarre, unnatural abilities, including necromancy and spreading a Hate Plague. Word of God has compared this to a Wolfbrother's powers in that it's a very primal form of magic, but exactly where his powers come from or how they work is mysterious. Word of God indicates that there is some specific supernatural force driving Fain, but hasn't gone into further detail, so this might be a form of Theurgy.
There are also a couple of nonhuman races in the setting that have their own forms of magic - the Ogier have Treesinging, which lets them craft virtually anything from living wood without harming the tree and also to bolster and encourage the growth of plants, and the Aelfinn and Eelfinn can answer questions and grant wishes respectively, though the exact means by which they do this is unknown, and are powered by human memory and emotion.
Mercedes Lackey uses a variety of magic systems in different series. Although most of her magic characters in any of her series have an inherent gift for magic, there are notable exceptions, e.g. Madame Arachne and her son Reginald of the Elemental Masters book The Gates of Sleep and the villain in the Diana Tregarde book Jinx High.
The Velgarth series (which includes the Heralds of Valdemar series), shows instances of Inherent (in the "mind-magic" Gifts of the Heralds, and the Mage Gift of her mages), Theurgy (both with the Shin'a'in Shamans and the Karsite Priests, as well as her northern "barbarian" tribes), Rule Magic (traces show up in most of the magic systems shown), Music Magic (in the Valdemar Bards, as well as the use of drums and flutes by the Hawkbrothers), Force Magic (the "high" or "true" magic used by the mages), and White and Black Magic (the Vkandis Priests and any of the magical Big Bads respectively, especially the Blood-path mages.) The idea of treating magic as a scientific endeavor, with predictable rules and outcomes, causes serious distress on the part of one of the mages, especially when it turns out to work.
In her Elemental Masters series, we see Elemental Magic, combined with aspects of Nature Magic (particularly for Earth mages), Force Magic, and Theurgy.
In her Tales of the Five Hundred Kingdoms series, Champions tend to make use of Device Magic, Witches and Hedgewizards are mostly Nature/White magic, while Wizards and Sorcerers (and their female counterparts) are more Rule/Theurgy magic. In the Five Hundred Kingdoms series, humans get magic when their lives start to resemble stories.
In the world of her The Obsidian Trilogy , as well as the sequel, The Enduring Flame, there are four major types of magic at work. Wild Mages use a combination of Theurgy and Wild Magic (what else?). High Mages work with a combination of Rule Magic and Force Magic. Elven Mages (perhaps the least-explained form of magic in the series) seem to work with pure Force Magic. Lastly, the demonic Endarkened and the corrupted mages who serve them use a Force Magic-oriented form of Black Magic, with Necromancy included in the whole charming package.
Magic in George RR Martin's A Song of Ice and Fire seems largely to be powered by theurgy (the two most flashily powerful sorcerers both seem to get their powers from the Lord of Light, and the warg abilities and green dreams of the North seem to be related to the weirwoods, known as the Old Gods) and force magic (magic went out of the world when dragons did. Now that dragons are back, magic is coming back in force.) Equivalent exchange is also made explicit, in the repeated line that "Only death may pay for life", and in the power of king's blood.
Though the use of magic in the series is intended to deconstruct Functional Magic, with magic largely serving as a mysterious influence without logic or form. Melisandre's POV chapter goes into considerable detail how uncertain and frustrating and unknowable magic is, especially for those who use it.
In Garth Nix's Old Kingdom series, there are a few types of magic. "Charter Magic" is strict Rule Magic. "Necromancy", with the bells, is Device Magic paired with Inherent Gift. "Free Magic" is less-strict Rule Magic, with an element of Wild Magic.
The "warrens" and "wards" in the Malazan Book of the Fallen are examples of Force Magic, although this may be Theurgy masquerading as Force Magic courtesy of all the magic in the series' Warrens being derived from the Elder God K'rul.
The witches and wizards of Terry Pratchett's Discworld typically avoid using magic, since it's ultimately all wild magic, so there's no guarantee exactly what will happen when you use it. When they do use it there tends to be a certain amount of rule magic to it, and the rules are often made more complicated by the wizards themselves, who invented most of them so that laypeople wouldn't get the idea that magic was easy and start trying it themselves — that, and all the spectacle and paraphernalia of magic really impresses the non-wizards.
The main reason behind this attitude is that the last time magic was used so casually, it led to the Mage Wars, which almost destroyed the world:
- That's why [magic] was left to wizards, who knew how to handle it safely. Not doing any magic at all was the chief task of wizards — not "not doing magic" because they couldn't do magic, but not doing magic when they could do and didn't. Any ignorant fool can fail to turn someone else into a frog. You have to be clever to refrain from doing it when you knew how easy it was. There were places in the world commemorating those times when wizards hadn't been quite as clever as that, and on many of them the grass would never grow again.
Harry Potter books use Inherent Rule Magic plus Alchemy, plus a number of magic devices, though it has been hinted that this sort of magic is just the beginning. The Unforgivable Curses would be Black Magic achieved through Rule Magic, Force Magic, or some combination thereof. Lily Potter's mysterious protective magics for Harry are explicitly described as Blood Magic, and most fans interpret it as the self-sacrifice variety. There are also traces of Wild Magic in instances such as the Ford Anglia spontaneously gaining sentience.
We also have Magic Music from the Merpeople. Really, Harry Potter uses all forms of magic except for Theurgy.
Mistborn series brings us Allomancy. Here, there are a collection of effects, but one must possess two things to perform them: a genetic knack and a corresponding metal in your body. Typically, an Allomancer can produce only one effect by burning only one metal. Mistborn, on the other hand, can burn all the metals, producing all the effects. The book also features Feruchemy, as system wherein someone can store up their own traits and abilities in "metalminds" and draw on them later as needed, and Hemalurgy, which allows abilities to be stolen from one person and added to another. Precise applications of this art can even be used to create entirely new species.
In Elantris, all magic is Force Magic powered by an energy called the Dor. There are several ways to access this energy, though — the Elantrians draw complex runic structures in the air, the art of Chay Shan can provide temporary bursts of strength and speed, and the Monks of Dakhor use a combination of runes and blood sacrifice. The novella The Emperor's Soul, set in a different continent on the same world, introduces two more- Forging, which can essentially rewrite an object's, or even a person's, history in order to change its present nature, and Bloodsealing, a form of necromancy that allows the Bloodsealer to not only reanimate the dead, but to allow their creations to perfectly track anyone whose blood they've sampled.
In Warbreaker the main form of magic is called BioChroma — it draws on an energy called Breath (which all people possess and can be given away at little cost) and colors in the environment to bring inanimate objects to life. Generally speaking they can be given only one specific command to follow, but sentient objects with permanent powers can be created with great difficulty, and animated corpses called Lifeless have intelligence similar to a robot or computer and can be "programmed" with more complex commands.
In The Stormlight Archive, the magic we've seen so far (only the first of ten books has been released) is powered by the titular Stormlight which is infused into gemstones by highstorms and either used to run devices called fabrials using the gemstones themselves, or some people who are apparently all bonded to special types of spren (spirits), if Kaladin's example is typical can draw out the Stormlight from the gems to use as Mana to fuel magical abilities. As it turns out, Soulcasting can be acomplished either way.
In The Bartimaeus Trilogy by Jonathan Stroud, magic is based entirely on Theurgy, although the practice of summoning and bargaining with djinn and other entities is governed by numerous Rule Magic-style elements (incantations, pentagrams, runes, etc.). Magical Devices, including several of great plot significance, get their power from having potent magical beings imprisoned inside them. Interestingly, magicians have conspired to conceal the theurgical source of their power from "commoners", playing up the Rule Magic aspects and heavily implying Inherent Gift (an outright lie). Among the titular djinni's greatest complains about magicians (and, by extension, all humans) is that they take credit for everything that the summoned spirits (not demons, whatever the magicians say) do. Additionally, the spirits summoned have their own powers, like Detonations. They can also shapeshift, and both would be considered to be Inherent Gifts. All spirits can do these to some degree.
In a very cool inverted example, a human is summoned to the spiris' realm. Just like the summoned spirits are endangered by staying in our world too long (they lose power over time), humans lose cohesion in the spirit world, eventually to a lethal extent. Spirits are much better able to survive in our world than we in theirs; mid-strength ones can be on the job for years on end without dying, but a human can't stay in the spirit realm for more than about an hour without dying, less to avoid permanent damage. By induction from this example, Theurgy is itself, on a meta level, Force Magic - humans and our realm are order, whereas spirits and their realm are disorder. Bringing spirits into the human world pains them by defining them, but they have powers to break the "rules" of science, whereas bringing humans to the spirit world damages the spirits because the humans bring order along for the ride, and damages the humans when they begin to comprehend and work with the disorder of that realm.
Harry Turtledove's Darkness Series, which depicts an alternate, magic version of the Second World War, uses Rule Magic (spells are weakened by proximity to water, while they are powered up when close to "Ley Lines") and Device Magic ("sticks" and "eggs", magical equivalents of guns and bombs, respectively), as well as some forms of Alchemy. The Nazi-analogue Algarvians also make use of a kind of Black Magic toward the end of the war, as a last resort; it's powered by mass human sacrifice, drawing upon the many ethnic prisoners they took over the course of the conflict. There's also a magical Manhattan Project, utilising heavily mathematical and rigorous investigation of the fundamental laws of magic, much akin to the study of physics.
The The Legends of Ethshar novels by Lawrence Watt-Evans have numerous different types of magic practised by different disciplines: Wizardry is rule magic (but with utterly unpredictable results if you bungle it), sorcery is device magic, Theurgy (used by priests) and Demonology are naturally inverses of each other, witchcraft and warlockry are two distinct flavours of Psychic Powers (the latter being slightly less flexible, far more powerful, addictive and invariably fatal in the long term), and then we have the less common magicians like the Ritual Dancers, Herbalists, Scientists, Necromancers, Prestidigitators... Several don't really count as magic to us, but do to most Ethsharites. According to the author, different authorities in the world claim the number of "distinct" magical types to be anything from 3 to 12, and the author usually claims "only" seven types. Magic in Ethshar is complicated.
Rule Magic — Telemain the magician constantly spouts magical technobabble, although most magic users get by on instinct without paying any attention to the rules he's so fascinated with. Morwen the witch approaches spells rather like cooking, just follow the recipe and you're done. She treats Telemain's obsession with theory as a sort of amusing quirk.
Wild Magic — the Enchanted Forest itself fits the description of Wild Magic, as does Mendanbar's semi-sentient sword.
Device Magic — magic mirrors, which play a large part. Also, witches and magicians are said to get their power from magical objects and ceremonies.
Inherent Gift — certain sorts of magic users, such as dragons, are born "generating" their own magic.
Force Magic — mostly Mendanbar and Daystar, who are able to sense the "shape" of magic and manipulate it at will. Also, their powers stem directly from the "ambient magic" of the Enchanted Forest, making it much more difficult for them to cast spells while outside of it.
The Illumination trilogy by Terry McGarry is unusual in that it's one of the few works that contains multiple types of magic but has neither theurgy nor wild magic. Magelight could be described as a combination of inherent gift, rule magic, force magic, and device magic, and in practice functions as black magic with Dark Is Not Evil employed. Heartlight is force magic and white magic, and can be learned by anyone. Mindlight is an inherent gift, mostly used for divination, and tends to drive the user insane. Interestingly, the three are best divided by the three most common presentations of magic, respectively magic as pseudoscience (complete with Magi Babble), magic as a connection to nature, and magic of an unexplained nature with deliberately vague capabilities and limitations.
Uses the True Name system, practiced by wizards who have an Inherent Gift, but still have to spend years learning all the Names in the Language of Magic (which is also the Language Of Truth, except when dragons are talking). Although no human can live long enough to learn literally all. One nice touch is that names change from place to place—a powerful spell from one end of the world will fizzle and die at the other.
A kind of Equivalent Exchange is discussed in one book: Ged is inquiring about the ability to change ordinary rocks into diamonds, which is apparently possible. The instructor's response is that Ged should consider what the consequences would be if all the islands in Earthsea were changed into diamonds, since the rocks they used to be comprised of would then be lost. This makes it easy to see how Reality Warping Is Not a Toy.
A lot of the flavor in The Case of the Toxic Spell Dump comes from its ubiquitous use of Theurgy, as it name-drops various gods, faeries and spirits constantly. Depending on the being invoked, a given spell may also constitute Rule Magic, Summoning, Alchemy, Transmutation, Equivalent Exchange, or White or Black Magic. When bound to objects, such as flying carpets or elevator shafts, spirits become catalysts for Device Magic.
The magic of A Wizard in Rhyme at first seems to be straight Theurgy, with wizards getting power from Heaven and Sorcerers from Hell (complete with literal deals with the devil), fitting well in a world where saints and demons occasionally interfere directly. Then later the heroes discover that some elements work like a standing electronic field, so it's also partly rule magic. Later still it turns out that pagans unaffiliated with either side can use it, and even the characters lose track of how it actually works.
Talent from The Night Angel Trilogy is an example of Inherent Gifts. Talent is also a form of Force Magic, since it recharges with the Sun. Also, several other forms of magic exist in-setting. The ka'kari, Curoch, Iures, Kylar's wedding earrings, and several other items are obviously Device Magic. Kylar's immortality/resurrection cycle are a form of Theurgy mixed with Equivalent Exchange, as is magic cast using the Vir. The Chantry uses Rule Magic, and all magic has elements of Rule Magic as well, particularly the Theurgy.
Bahzell series, magic is done by manipulating the energy contained within just about everything, á la Force magic. The catch is that energy in inanimate things like rocks is harder to manipulate than in animate things like people. There's also something called "wild magic" that just lets the wild mage use all kinds of energy effortlessly. Those devoting themselves to a particular god may also get power from him/her.
Trainee (child) magicians in Diana Wynne Jones's Chrestomanci books learn rule-based, force, and device magic at school. Mistakes can lead to wild results (and punishment). It is implied that anyone can manage the simplest device magics, although Cat fails miserably probably because Enchanter's magic is demonstrably quite different. Even Janet who is from a related non-magical universe can grasp the basics.
Patrick Rothfuss's The Name of the Wind features an interesting form of Rule Magic. It's based on the concept that you cannot create or destroy energy, and all of the force in your magic has to come from somewhere, ranging from a fire to your own body. Kvothe doesn't consider sympathy to be real magic though, it's just something it's possible to learn how to do. There's also alchemy, which seems to be an entirely parallel version of chemistry with some extremely strange effects, but is still Rule Magic. Sygaldry is also mentioned, but is really just a set of rules for applying long-lasting sympathetic bindings to inanimate objects. The magic of myth and legend and fireside stories in the setting is a True Name system which is incredibly difficult, requiring not so much the learning of names but the study of how to find them when you need them, because they change continuously.
In Dragonlance Wizards use Rule Magic (which is really just Vancian Magic, as the setting is a DnD setting) Primal Sorcerers and Mystics could be considered to use a form of Force magic, and Clerics use Theurgy. There is also Device Magic in the form of many magic items. Technically speaking, Wizards get their magic from the gods of Wizardry.
In Jaida Jones and Danielle Bennett's Havemercy magicians of Volstov have Inherent Gifts powered by Force Magic from a source called "the Well". There are also mechanical dragons. Ke-Han magicians use Elemental Magic but how they power and/or focus it is a mystery.
Lev Grossman's The Magicians has heavily rule-based magic, in which young mages are required to memorize information on the factors that effect their spells from massive books before they can cast them. In fact, an entire year of their education is spent learning how to calculate these factors and act upon them without even thinking about them.
Several kinds from the Chronicles of the Kencyrath. Shanir, like heroine Jame and her twin brother Tori, have Inherent Gift, granting them powers that can range from healing to claws to supernatural bad luck. Priests use theurgy (if they're of the Three Faced God) or force magic (of the other gods, as those gods are actually shaped from ambient energy by their followers beliefs). Then there is the world itself, which is filled with wild magic, which powers both supernatural events and creatures and can be tapped in to by sorcerers (like Matriarch Rawneth) via rule magic.
From Codex Alera, the human civilization uses a strange mix of inherent gift and theurgy (elemental spirits called furies do all the heavy lifting, but all Alerans have the innate ability to summon and command them). In the same world, the Canim Ritualists use rule magic powered by blood, while the Marat have the inherent gift of forming empathic bonds with other life forms.
Magic in Robert E. Howard's Conan and Kull stories seems to be Rules Magic, usually focused in a device like Thoth-amon's ring or the Heart of the Elephant. Alchemy also plays a big role. And it's always Black.
There are three main branches of Rule Magic in The Saga of the Noble Dead — thaumaturgy deals with physical matter, conjury with natural and elemental spirits, and sorcery with the mind and soul. The three can be combined to produce more advanced effects (necromancy, for example, is said to involve both sorcery and conjury). There are also three ways to cast magic — spells produce weak but instantaneous effects, rituals are more powerful and last longer but also take longer to cast, and artifice allows items to be imbued with permanent powers. All undead (and some humans and elves) also have Inherent Gifts of various types. Theurgy is also said to exist according to rumor, but whether it actually does or is just a variant usage of the above is not yet clear.
In Monster, the most common form of magic is predominantly Rule Magic, utilised with either runes, gestures or incantations; it can be used by just about anyone, though it takes a good deal of education to make a living out of it. However, given the current state of magic in the world, most people in the world are unable to even see the supernatural in action, and those who can have a lot of trouble remembering spells — hence the eponymous character's rune handbook. Following the death of Lotus, The Magic Comes Back, allowing Muggles to see supernatural activity and removing the memory haze.
In the Winds of the Forelands series, magic is mostly the province of the Qirsi, who have a variety of different kinds of inherent gifts, divided into Deeper and Lesser powers. Most Qirsi have only a couple of these powers, a rare few called Weavers have them all. Using any power saps the Qirsi's life energy, which is why they a frailer and shorter-lived than the non-magical Eandi:
Gleaning: Lesser power, common to almost all Qirsi, lets them see snatches of the future. This ability can be further focused using a special crystal called a Qiran.
Fire: Lesser power, allows the Qirsi to summon and control fire.
Mists and Winds: Lesser power, allows the Qirsi to control the weather.
Shaping: Deeper power, allows the Qirsi to reshape or destroy physical objects by force of will.
Lnaguage of Beasts: Deeper power, allows the Qirsi to communicate with animals.
Mind Bending: Deeper power, allows the Qirsi to use what amounts to a Jedi Mind Trick (against other Qirsi) or complete domination (against Eandi).
Weavers: The rarest and most powerful Qirsi have all of the above powers, plus the ability to know what powers another Qirsi has by looking at them, to enter the dreams of other Qirsi, to control other Qirsi's magic with or without their consent, and bind the magic of many Qirsi together for extremely powerful feats. They're also generally less squishy than other Qirsi. Big Bad Dusaan is one, as is The Hero Grinsa.
The Sequel SeriesBlood of the Southlands introduces a second Witch Species, the Mettai, an offshoot of the Eandi who practice Blood Magic. They're abilities are generally more flexible and less defined that the Qirsi's, but they have less raw power. Mettai magic doesn't shorten the caster's life, but they have to bleed themselves beforehand and chant a short incantation specifying what effect they want, whereas for a Qirsi it just takes an act of will.
In China Miéville's Kraken some of the cult are able to use Theurgy. There are also a number of people with Inherent Gift, some of whom channel it through Rules Magic and there is the odd magic item or two as well, like the Star Trek phaser that actually works.
In Adrian Tchaikovsky's Shadows of the Apt series all the kinden have inherent gifts, some of which, like flight are shared by several races, others of which like the Ant's telepathy or the Wasp's energy blasts are unique to the race. The ability to use magic is itself an inherent gift that only some of the kinden like the Moths or Mosquitoes can use. The Moths magic seems to be more in the realm of Psychic Powers (clairvoyance, dream visions, Mind Control) while the Mosquitoes, no big surprise, use Blood Magic. Meanwhile the ability to comprehend, use or create technology is itself a gift only the Apt races can use.
The Circle of Magic series by Tamora Pierce had ambient and academic magic. Both are inherent, but academic magic is more rule-based, while ambient magic is more nature magic with some aspects of wild magic.
To clarify, ambient magic is more like Force Magic. The key difference is that an academic mage mostly has their power come from inside themselves and thus are free to pick a magical specialty. An ambient mage already has their power tied up with something, which can range from plants to weather to even dancing, and rely more on drawing power from outside sources. Whereas academic mages have trouble building up their powers, ambient mages struggle to control a great deal of power that's constantly flowing into them. Also ambient mages only account for 25% of the mage population and most "magic sniffers" don't recognize ambient magic in children. In fact, most people aren't even aware of ambient magic's existence.
Also, all magic is inherently somewhat wild, as it's made clear that you can't really defy nature and doing so has disastrous consequences.
There's explicitly mentioned device magic. Mages are able to make objects that Muggles can use for magical effects.
In Doctrine of Labyrinths, there's a little bit of everything. Most of the wizards/practitioners have an Inherent Gift (and the ungifted are called annemers), and how/why they use their magic very strictly depends on the school to which they belong. One of the main characters, Felix, has an extremely powerful inherent gift, and uses Rule Magic to get what he wants done, except, according to his school, the Cabaline, any use of magic upon a fellow human is heresy. Furthermore, the Cabaline also use a device called the Virtu to anchor and channel their spells. Another group, the Corambin practitioners, use a combination of Inherent Gift, Rule Magic, Force Magic and Device Magic to manipulate what they call "aether" or "vi" that exists in all things, or to power some very cool steampunk devices. Yet another nation, the Troians, have an entire sect devoted to Divination and dream magic, and even have a sort of celestial garden in which dreamers can sort of, you know, hang out; yet another sect of wizards use Tarot cards for divination. There is also a discussion about what magic is, really. Felix defines it as an elemental, ambient force manipulated via metaphors; there can be good metaphors, or harmful metaphors, but bad metaphors simply won't work. There is also an interesting dichotomy between light and dark magic, clairance and noirance. It is explicitly said that clairance isn't necessarily good, nor is clairance necessarily bad; they exist as two differing categories of magic. Felix, himself, is particularly gifted in noirant magic; he's a natural at necromancy, and uses his gift to lay the dead to sleep. Finally, there's some Summoning Magic involved: one could summon an evil spirit, called a rachenant or fantome, to do one's bidding, but it will generally subsume the summoner's will or one could just latch on to you because you look tasty.
The Kane Chronicles is mostly Rule Magic with a return of Theurgy with hints of Force Magic. Wizard used words and rituals to effect reality and draw upon their own reservoirs or stored magic. Its effectiveness is tied to Ma'at, or the order of the universe compared to chaos. Theurgy was forbidden for centuries and the gods imprisioned, but recently has made a come back.
In Krabat, magic is rule magic based on words, gestures, drawn signs and a few other bits, with some Theurgy.
The Three Worlds Cycle uses underlying Force Magic, with some Alchemy and Device Magic based on it. Simply put, magic is mediated by a weak force, emanating from "nodes", which are magical sources linked to geographical features. People can draw on this weak force, but risk aftersickness or, worse, anthracision (being burned alive from the inside out) if they draw too much. Nodes also produce 3 strong fields at right angles to each other, which are beyond the grasp of human control (they would cause instant anthracision).
In the Well Of Echoes, the second quadrilogy, walking tanks known as "clankers" run on this weak force, channelled through specific crystals and guided by a controller. Hovering Aachan "constructs" also run on the weak force, but have specialised machinery to channel the strong forces to fly.
There's also a more direct form of magic called Geomancy that the protagonist of the Well Of Echoes, Tiaan, uses: rather than rely on the omnipresent field to do magic, it relies on one-off geographical activity and the energy it produces to produce effects: for example, Tiaan manages to conjure up a heat ray from a crystal by tapping into a stalactite breaking off the ceiling of a cave and falling into a lava pool.
In An Exercise in Futility, Conservation of Mass and Energy is tweaked to include magic. A chemical called seidrium stores magical potential. With proper training, seidrium can be converted to just about anything.
Erna, the world of The Coldfire Trilogy, is saturated by a mystical energy called the Fae, which responds to the human subconscious. Humans can learn to manipulate the Fae via rule magic, becoming sorcerors, and some are born with the inherent gift of seeing the patterns of the Fae, making them natural sorcerors (these people are referred to as Adepts). It's also possible to break the normal rules of magic after making a sacrifice of some sort- the greater the sacrifice, the greater the power. All Fae can be considered Wild Magic. There are four basic kinds of Fae:
The Earth Fae is the most commonly used, and is comparatively stable. Most human sorcerors and adepts use this kind of Fae.
The Dark Fae is only accessible at night or underground (hence its name- it is far more powerful than the Earth Fae, but also far more volitile- humans who aren't careful can end up causing it to spawn horrors simply through undisciplined thought. It is usable, with difficulty, but the only real master of it is Gerald Tarrant. Generally considered Black Magic. The eponymous coldfire is the essence of the Dark Fae.
The Tidal Fae is connected to the motions of the planet Erna itself. Its power varies greatly- sometimes it is the most powerful form of Fae, and sometimes its barely there at all. Humans can't use it, but the Rakh can, especially the females, who do so instinctively. In the second book, it is revealed that some human adepts are beginning to be born who can use this form of Fae.
The Solar Fae is connected to the sun and is immensely powerful, but can only be accessed though acts of tremendous faith on the part of humans. The church of the One God, though it frowns on most forms of Fae, maintains stockpiles of weapons and artifacts which have been empowered by the Solar Fae. Generally considered White Magic.
Septimus Heap has two different kinds of Magyk, a Witch and a Wizard one that are themselves split in a Darke and a non-Darke fashion. Both kinds can be used by professional Wizards/Witches and non-spellcasters alike, but with several limitations for the latter. Also, most spells can be encoded in objects called Charms.
The magic in the Alex Verus series seems to be of the 'Inherent Gift' type. Mages can use one and only one type of magic, which is determined by their personality. The protagonist uses divination, elemental magic seems to be common, and other types are hinted at. The author describes the system here.
The NeverEnding Story uses Inherent Gifts for certain supernatural creatures (Luck Dragons, the Childlike Empress, and even regular humans when inside Fantastica). Human imagination is also a form of Force Magic, which is why humans have special powers when inside Fantastica. Also we have Device Magic in the form of the Nevereding Story book itself. The AURYN also has the power to grant wishes, as it is an extension of the Empress' power, which could be considered a form of Theurgy.
Lauren Buekes' Zoo City combines Inherent Gift with a twist on Theurgy and Force Magic. "Zoos" get their powers from their animals which are a form of familiar. The twist is that they didn't make any conscious deal to get their Animals; they were bestowed on the zoos for committing violent crimes by a mysterious force called the Undertow. There are also shamans who receive visions through Alchemy.
In Charles Stross' The Laundry Files, applied thaumaturgy is a branch of higher mathematics, and thus is Rule Magic. Alternate universes can be accessed by generating a complex geometrical curve either by mind alone or through the use of computers (Device Magic), which can be anything from cryptological supercomputer nets to smart phones to more esoteric implementations such as games of fairy chess. Some of those universes are utterly different to our own, but the beings that live in them can be communicated with or summoned (Summon Magic and Theurgy). The series contains examples of:
Divination: The Predictive Branch of the Laundry uses a mixture of traditional (crystal balls, entrail reading) and modern (web-cams pointing at crystal balls, stochastic mapping of Tarot card readings) to get a roughly 50% hit rate.
Mentalism: Geases of various sorts, most prominant of which is the Laundry warrant card which at one level works like psychic paper, and at another can be invoked to bind the mouths of witnesses to occult phenomena.
Necromancy: Extra-dimensional entities are summoned to animate the bodies of the dead. More powerful ones can also possess the living, displacing the original inhabitant or consuming them.
Blood Magic: If one is not mathematically inclined, the entropic decay caused by suffering and death can be used to power magic.
Music Magic: The series contains one specially-constructed musical instrument, the Eric Zahn violin, that is used to exorcise possessing entities, through the representation of mathematics in musical form (and a little blood magic).
Black Magic: Arguably. While the Laundryverse contains god-like entities, they are inimical to lesser beings such as ourselves, seeing our suffering as fuel for their continued existence or resuscitation. The morality of magic is purely human imposed.
There are three main types of magic-user in The Powder Mage Trilogy by Brian Mc Clellan. All three types have a "third eye" that allows them to "see" magic (and identify other magic-users), in addition to more specialized abilitiyes. The types are:
Privileged: The most powerful, and rarest. Basically the closest to traditional wizards, they have a wide range of elemental powers and a Priveleged is basically treated as a Person of Mass Destruction. They cast spells using elaborate hand gestures rather than spoken incantations, and a Priveleged can usually be recognized by their distinctive rune-stiched gloves. The Predeii- immortal predecessors of the Priveleged, some of whom are still running around- also exist. They're very similar to ordinary Priveleged, except that they're a lot more powerful.
Marked: Also called Powder Mages, who have power based on gunpowder. They can ingite it (or prevent it from being ignited) at will, have limited telekinetic ability in regards to projectiles fired from a gunpowder weapon, and can inhale gunpowder to enter a kind of trance that enhances their phyiscal and mental abilities. They also have a limited ability to disrupt Priveleged magic, which is one reason Priveleged don't like them much. Though not as versatile as Priveleged, a Marked equipped with firearms is extremely dangerous- and they live in a world that averts Medieval Stasis and Fantasy Gun Control.
Knacked: The most common (comparatively speaking) and weakest. Knacked have one magical power, usually a natural trait or skill enhanced to supernatural levels. There are many kinds of Knacks, but being able to go indefinitely without sleep, having a perfect memory, or being able to pick locks without a lockpick are all examples.
Other kinds of magic-user are hinted to exist, but the main three are the only ones who get much face time- except for Ka-poel, a "barbarian" girl who has a form of extremely potent sympathetic magic that can defeat even Priveleged. As she isn't terribly keen in sharing information on her powers (and is mute on top of that) it's unclear exactly how her magic works, har far her powers go, and how common it is in her homeland.
Primarily Inherent Gift in The Mortal Instruments, as one of the defining attributes of being "human" is the inability to use magic and thus free access to magic is generally limited to Downworlders and Shadowhunters. Warlocks (who are half-demon) are the primary practitioners of magic, although the Shadowhunters have their Runes and the fairies possess strange powers.
Played pretty straight in Destined to Lead, even going so far as to outright state what the rules are. Interestingly though, unlike most Rule magic, one of the rules is 'There are no such things as magic words, magic is conducted solely by feeling, so everyone can say whatever they want.' Hence- you get spells like "Burn!" and "Ha-shè!" in the same book.
In The Broken Crescent, the Language of the Gods is the programming language of reality, and speaking or writing it causes magical effects.
Magic in Fates Road works, and everyone knows it works. However, it's illegal and only practiced by criminals and sorcerers who live underground.
All magic in Larry Correia's Grimnoir Chronicles is force magic in that it's based on a symbiotic relationship with the Power, an other dimensional Energy Being of vast...power but it's expressed in ttwo different ways. Acives express it through Inherent Gift while kanji and runes are a form of Rules Magic that give powers to non-Actives, increase the power of Actives or give an Active a power they wouldn't otherwise have.
Sergey Lukyanenko and Nick Perumov's novel Wrong Time For Dragons has the Middle World be full of magic. The most powerful magic is Elemental. The four Elemental clans rule over most of the human lands, while the numerous Totem clans are scattered throughout, most lacking any unity (like their chosen animals). The most organized Totem clan is the Cat Clan, who have carved out a small parcel of land between three of the Elemental clans' lands and use their cat-like wiles to have enough political influence to play the game on equal footing with the Elemental clans. In the lands of the Elemental clans, the mages use their power over their respective element for the benefit of the people. For example, the fields of the Earth Clan always bring bountiful harvests, while their mines never run out of valuable resourcs. The capital city of the Water Clan is a wonder full of beautiful fountains, canals, water mirrors; every night a refreshing light rain washes away the dirt into the sea.
Inherent Gift is rare because it follows specific bloodlines. Bladicraft, for instance, can only be used by members of the Bladi Clan.
Rule Magic is the most common variety practiced because anyone can learn it if they have a teacher or a book. It's called "magecraft" and it involves a lot of studying. The most important lesson is the Three Laws of Magecraft; Mana, Knowledge and Will Power. The second most important is that Rule Magic is a crutch for learning Force Magic. Rules make performing magic easier for beginniners. Experts don't need them.
Alchemy is ambigious. Since the study of mana is as old or older than the study of chemicals, no one bothers with a difference.
Device Magic is also common. Wards against spells and physical harm are often sold to warriors while an artist is more likely to buy something to asist their latest work. Both of them stop by the corner store.
Force Magic is present in pulling mana from the surrounding enviroment or from a Place of Power, but most mages are only good enough to pull it from their own soul. Once a mage has a sufficient level of skill and power, they can forgo Rule Magic and focus entirely on Force Magic.
White Magic is called "healing magic" while Black Magic is called "combat" or "battle magic". There is no color for magic that is neither.
Blood Magic is a downplayed example. Only the blood of Basilard or his relatives count because their blood is magical. The blood of someone like Eric is useless for magical purposes.
In The Craft Sequence the eponymous Craft is Force Magic, powered by different sources, with the gods of the setting drawing from the souls of their followers, and Craftspeople drawing from starlight and the earth itself. These power sources let Rule Magic work, in the form of contracts, which further allows Device Magic, Theurgy, and other magical effects to work.
Live Action TV
Supernatural has used virtually every flavor of this at some point in time, from magic items in curse boxes to Sam's assortment of psychic powers, to spells, sigils, and incantations that do everything from exorcising demons to allowing Dean to hear the thoughts of animals.
On Bewitched this was a case of Inherent Gift specific to a Witch Species, although occasionally other magical creatures did show up. Ordinary humans could not learn to use magic, but could be granted magical powers by a witch or warlock.
Buffy the Vampire Slayer and Angel have shown all of these. Alchemy and theurgy were the most popular, as most spells required some kind of plant or animal part. Spells that didn't generally required dealing with gods or demons. There were a few that used Rule Magic. Also, while one could train in magic, and those people usually got telekinesis, there was one girl in Angel who naturally had telekinesis as an Inherent Gift and another who generated electricity the same way. Witches seem to combine Theurgy and Inherent Gift. Plus, there are the natural abilities that every demon has. There were even a few cases of Wild Magic, such a girl who felt she was invisible turned literally invisible, plus all those ghost hauntings.
The above instance of a girl turning invisible is due to the Hellmouth, which is a nexus of supernatural energy. Thus it is also force magic. Also, while Willow sometimes invokes goddesses it's not clear whether she's actually drawing power from them or even if those gods exist. But Theurgy is played straight with Osiris, who personally makes an appearance in season 6. However Theurgy of a different sorts is also used and there's one episode where a bunch of JerkAsses were going to sacrifice a girl to a demon in return for money and power.
Charmed uses all the types of magic. Potions are Alchemy and Eye of Newt, and some spells require reagents, too. Real witches have an Inherent Gift, as do demons and other supernatural creatures. There are specific rules to magic such as it being triggered by emotions, and phases of the moon and time are also mentioned. We also have Force Magic with things like the Nexus, and the novels expand upon saying that non witches can tap into ambient sources of power (such as the Nexus) and cast spells. We have Theurgy of sorts whenever people make deals with demons in return for superpowers. There's also device magic, for example a mist that will turn a mortal into a Physical God. Finally, all magic is wild to a degree, and there are several instances where the sisters have tried to make their lives easier with magic only for it to inevitably screw up.
Furthermore, many Power Rangers are powered by Device Magic, (e.g., magical coins in their transformation devices, a magical crystal powering all of their technology) and it turns out that all Rangers, regardless of whether they use magic or technology or both, are powered by the Morphing Grid.
The Faery magic in the 1998 Merlin series was shown in the actual series to be mostly Rule Magic that could only be used by fairies. Wizards used either Theurgy (getting their powers from The Fair Folk) or Inherent Gift (if they were half-fairy themselves, as Merlin was). Wizards were ordered in power depending on how they called on their magic; weak wizards used words, intermediate wizards used gestures, and the most powerful wizards only had to think. The novelizations expanded on the system quite a bit, in that fairy magic was mostly illusion, but a half-human, half-fairy could combine fairy illusion with human feeling to create much stronger magic.
Out of This World uses Rule Magic for gleeping and Inherent Gifts for Evie's other powers.
Present on True Blood. Inherent Gift seems to be fundamental to exactly how much magical power one can truly achieve without additional help. For example, Marnie was a mediocre practitioner of Rule Magic at best despite a lifetime of practice until she was possessed by Antonia, whereas Lafayette seemed to exhibit considerable magical potential without any training. Fairies and at least some of their part-human descendants also have an Inherent Gift for Force Magic. Maryanne the Maenad employed powerful Theurgy and Blood Magic as part of her worship of Dionysus.
Wizards of Waverly Place: Formulaic Magic and Item Magic. It's strongly implied that the incantations mainly serve to focus the thoughts of the wizard on a specific spell and aren't strictly necessary.
In American Horor Story Coven the witches rely mainly on inherent Gifts along with some Ritual Magic and Alchemy while the voodoo practitioners use a mix of ritual and Alchemy although some Theurgy is implied as well.
Divine magic users (Clerics and Paladins) mainly use Theurgy.
Wizards use Rule Magic, and in the earlier editions, this was Vancian.
Sorcerer magic was Inherent Gift magic with the same kind of Vancian system.
Warlocks use Theurgy in a different fashion than the Divine guys. In Third Edition, this was Inherent Gift magic similar to the sorcerer's, but with a more demonic flavor.
And of course, there's Device Magic in the form of more magic items than you can count.
Psionics, while called something other than magic, is essentially a Force Magic that uses the same energies and principles as magic, doesn't work in an Anti-Magic field, etc. In third edition at least, you had the option of treating Psionics as something different such that one couldn't directly counter or dispel the other one the same way they counter and dispel their own type of power. In practice though, it was easier to treat it as the same stuff accessed a different way.
On top of those are: Incarnum, which is sort of a mix between Theurgy and Force Magic, calling the soul energy into forms centered on specific parts of your body.
Binding: Binding extradimensional entities called "Vestiges" to yourself, a form of Theurgy
and Shadowcasting, a form of Force Magic, with perhaps a tad of Innate Magic thrown in, centering around using the shadowy shadowstuff of the Plane of Shadow to make...shadow...magic.
Artificiers used Rules Magic via Device Magic (their magic worked by applying magic enhancements to objects on the fly, so instead of casting Fly on yourself, you'd make your boots into Boots of Flying).
Vampires use Inherent Gifts, with some covenants (and one bloodline) practicing a strange form of Theurgy based around blood magic.
Mages use Force Magic laced with Rule Magic (and by a different set of rules than the mages of the old World of Darkness).
The SourcebookNight Horrors: The Unbidden also goes into how magic can go wild either in terms of a mage losing control of their own power, or spontaneous and inexplicable magical phenomena occurring. The reason for the latter can be anything from the result of a big magical battle, to power accumulating over time, to spirits passing between dimensions, to just because.
In the Second Sight supplement book, various forms of lesser kinds of magic are also mentioned, including Alchemy, Psychic Powers, and a Cosmic kind of Equivalent Exchange. You don't want to know what you have to do for some of the higher ranked spells/rituals from the Cosmic magic list.
Werewolves straddle the line between Inherent Gift, Rule Magic, and Theurgy — their powers are supposedly inherent to their nature, but with only a few exceptions they must be learned from spirits.
Hunters... well, it depends on the Conspiracy. The Lucifuge use Inherent Gifts based on the fact that they're the children of Hell. The Cheiron Group uses Device Magic based on cutting parts out of supernatural entities and grafting them on to themselves, whereas the Aegis Kai Doru's Device Magic is centered around the retrieval of ancient relics. The Ascending Ones use Alchemy to concoct elixirs that bestow them with unnatural talents. The Malleus Maleficarum use a form of Theurgy involving rituals associated with saints. The Vanguard Serial Crimes Unit uses Psychic Powers that aid interrogation and detective work. And so on.
Sin-Eaters appear to use Force Magic; they draw upon forces present in the Underworld and filter them through certain Manifestations to produce effects. They also practice Necromantic rituals that allow them to interact with, bind, and repel ghosts.
Mummies have two types of magic: Affinities, which are Inherent Gifts flavored with Wild Magic, innate powers that can be gained or lost at the whim of Fate, and Utterances, a form of Force Magic enabled by the strength of a mummy's life force, said to come from sources as old as the universe, and perhaps even older still.
Demons use Rule Magic based around utilizing the pre-existing occult physics of the World of Darkness.
Magic in Unknown Armies is almost entirely Rule Magic, although, crazy as most magic users are, they often believe that they're using some other system. There is some wild magic as well, mostly used by Non Player Characters. Device magic does exist, but it's rare - imbuing an object with magical power so that anyone can use it is a difficult process, either because it involves long, complicated rituals, or because you need the collective belief of millions of people to imbue an object (say, a holy relic) with great symbollic significance, or because they're spontaneously created during events of extreme emotion that coincide with a release of magickal energy and are thus irreproducible.
Magic in Shadowrun blends Wild Magic with several of the other systems, most notably Force Magic; magic is an unstable, quasi-living force that can sometimes simply cause things to happen (as with The Awakening), but it can be controlled either through complex formulas (as practiced by mages, the setting's Rule Magic users) or by interacting with one of the aspects of magic (as shamans do; they practice Theurgy). As well, there's a certain level of Inherent Gift involved, as only certain people are able to become mages or shamans, those with a particular affinity for the astral plane. Later supplements imply that the only reason any of this works is because the magic user believes it works, and that people who are particularly attuned to magic are capable of creating entire magic systems of their own (which makes it more Clap Your Hands If You Believe mixed with Inherent Gift).
Warhammer has an interesting combination of these. The Negative Space Wedgie at the poles cause the local equivalents of the arctic and Antarctic regions to essentially be overrun with Wild Magic. This is spread through the world by the "winds of magic" which can be tapped into by wizards as a power source (Force Magic), to power learned spells (Rule Magic) or enchant items (Device Magic). However, the ability to work these kinds of magic is itself an Inherent Gift that a tiny fraction of individuals are born with, albeit one that generally needs training and perfecting.
There are also a number of priests and shamans who practice a kind of Divine Magic, though the lines are blurred here as to whether it is something different from the usual magic of regular wizards or just the same kind of Rule Magic / Force Magic with a religious aesthetic. Empire Warrior Priests, for instance, can call upon the wrath of their god Sigmar to create minor magical effects in battle, and rules-wise this is treated slightly differently to normal magic (and the priests themselves do not count as wizards). Conversely Khemrian Liche-priests make invocations to their ancient gods, but their powers are treated as out-and-out magic and they do count as wizards (the same with Ogre Butchers, Orc and Goblin Shamans and Skink Priests). Many Dark Magic spells used by Chaos Sorcerers and Dark Elf Sorcerers also involve pacts with daemonic beings for their power, though this is not the sole means by which either type of wizard works their art.
The essential problem is that what would otherwise be relatively simple force magic is complicated by the fact that the force itself is 1. Sapient 2. Chaotic (both the math version and the alignment version) and 3. Made of daemon-gods that consider you, at best, an amusing plaything…
The equivalent to magic in Warhammer 40,000 can loosely be described as a combination of Wild Magic and Theurgy. Only replace "Wild" with "Horror". With training it can be made to look a little like force magic but, as with Warhammer magic, the force drawn upon is alive, aware, and abominable.
The horror aspect is most closely associated with the theurgical form, which is why all the "civilised" races have banned it, but that doesn't mean horror can't happen anyway, since the wild form involves using the caster's own willpower to enforce order on the literal embodiment of chaos from where all psionic power originates. Bad Things happen if their concentration slips even momentarily.
In Deadlands, almost all magic is some form of Theurgy, powered by either deities and nature spirits (good spirits), or manitous (evil spirits). The most peculiar one is the hucksters' magic, which is performed by engaging the demons in a test of wills disguised as a psychic game of skill and chance (99% of hucksters prefer poker). If the magician wins the card game and the demon loses, it must do something at his bequest, and if the manitou wins, it wreaks havoc. Non-Theurgy examples often use Theurgic elements:
Tempests, greenies, and sykers are all Inherently Gifted, with sykers incorporating elements of Force Magic.
"Enlightened" Martial Artists (read: Chop Sockey fighters) believe they're using their Life Energy to brutal effect, but it's actually a type of Force Magic.
In the After the End setting of Deadlands: Hell on Earth, there are witches, who aren't a species, but instead use a blend of Alchemy and Rule Magic. Contrast certain Mad Scientists in The Weird West, who were exclusively alchemists (with less-than-pure Theurgic inspiration).
Most of the "technomagic" in any of the game's three settings uses Device Magic mixed with one or more other types; there are also relics, which are made magical through a variety of means, but typically remain so forever (and can be used by anyone).
Dragon Dice features a setting in which literally any playable unit has the potential to use magic - there are specialized units that can more reliably utilize magic, but given the right results, any unit can produce magic results that can be used to cast spells. It is a system of Elemental Magic where a unit's magical capabilities are determined by the elements that it is comprised of on a basic level.
GURPS uses a combination of Force Magic and Rule Magic. In GURPS Magic various other systems are detailed, culminating in "Syntactic Magic" which basically lets you do whatever you want whenever you want (or at least try).
Rifts uses pretty much every flavor of Functional Magic in the list above. The main commonality is that all magic users act as living batteries of Mana (called Potential Psychic Energy or P.P.E.), which they can tap to power their spells.
Many magic users (the Ley Line Walker being a classic example) use Rule Magic in the form of Spells or Invocations that must be memorized by the user. However, unlike in D&D's Vancian Magic system, wizards don't have to study their spells every day.
Mystics have Inherent Magic: all their magic and psychic power comes from within themselves, and they can't learn spells like other types of mages can.
Shifters are a combination of Rule Magic and Theurgy. They learn spells like Ley Line Walkers and other types of wizards, but they focus on summoning and control magic and can make contact with powerful beings (usually evil, but not always) to gain even greater power for themselves. The Priest class from Pantheons of the Megaverse are a more classic, god-granted, form of Theurgy.
Alchemy is rare; while magic potions can sometimes be found in the game (and the Philosopher's Stone makes an appearance), Druids out of the England Sourcebook are about the only character class able to make potions.
Force Magic is something available to just about every single magic class, by way of Ley Lines and the eponymous Rifts, which are near-limitless sources of magic power a mage can tap into to enhance his own store of Mana. Likewise, proximity to a Ley Line or Ley Line Nexus increases the power of magic and psionics. Some classes, like the Ley Line Walker, have powers that can only be used when close to or on a Ley Line. Magic users who can't tap into Ley Line energy are the exception, not the rule.
Ley Lines and Rifts are also behind Wild Magic, in the form of Ley Line Storms, which is basically when the buildup of magic energy along a ley line goes critical and all Hell breaks loose, sometimes literally. Wild Magic was much more prevalent during the Time of Chaos immediately following the Coming of the Rifts, when magic was nearly impossible to control, and made the random dimensional anomalies and disturbances of the main setting seem sedate by comparison.
Device magic exists in many forms, from magic scrolls to rune weapons, but the most prevalent form of Device Magic on Rifts Earth is Techno Wizardy; which combines magic and technology to create Flaming Swords, guns that fire force bullets, and vehicles that run on magic energy.
Rifts: Underseas has whale magic, as in magic performed by whales. No, really. It's probably the closest the books come to Music Magic.
Most of the styles are relegated to specific classes. Elemental magic is the realm of Warlocks, Necromancy is used by, well, Necromancers, and Nature Magic is used by a few classes here and there (like the Old Believer of Mystic Russia). Summon Magic can be used by most wizards, but Shifters specialize in it. White and Black magic are mostly judged on a case-by-case basis, though Necromancy is mostly always evil, and Nature Magic is mostly always good. Shifters are generally considered to perform Black Magic, but that's more of a stigma attached to the class than anything inherent in it. Divination is available to some classes, like Temporal Wizards, but is mostly found among psychic characters, as is Mentalism. Transmutation isn't used very often, and Equivalent Exchange is more or less non-existent.
Exalted uses all of these in one form or another, but the most predominant forms are Inherent Gifts (in the form of Charms, innate abilities that allow an Exalt to pour their natural talent into their skill set/draw on the true potential of their physical form/emulate the demonic masters who gave them their power, depending on the type of Exalt) and Rule Magic (in the form of Sorcery, which basically allows the sorcerer to hack the raw source code of Creation and reshape Essence into whatever form she sees fit).
There's also thaumaturgy, a combination of Force Magic and Alchemy, with a hint of theurgy (especially for the Arts dealing with various spirits). Generally weaker than the other kinds, and often requires expensive components, but can be learned by anybody (some rituals are so basic and straightforward that they don't even require initiation, just the barest degree of occult knowledge) and has a lot of homely utility.
In Ironclaw Elemental magic, thaumaturgy, mind magic, and basic White Magic (despite being practiced by priests) are all a combination of Inherent Gift and Rule Magic. Necromancy on the other hand is Theurgy with an element of Wild Magic as it binds angry and often unwilling spirits for power. The "Book of Mysteries" supplement has other forms of Theurgy with different levels of risk, from offensive spells with Lutarism, to some particularly vile spells for Druids but not elemental attacks, to practically no risk for the secret prayers by the same Church that uses white magic.
Drakengard does not use Force Magic or Wild Magic. It has a form of Theurgy (pacts), Rule Magic (casting curses and seals), Alchemy (magic potions are sold everywhere), Device Magic (all equippable weapons can cast a certain spell imbued in them), and some people seem to be better sorcerers for no other reason than they happen to have an Inherent Gift, though it doesn't rule out others becoming sorcerers.
In Suikoden the magic system is definitely a Rule Magic of sorts: all magic in the setting is based off of the invokation of "Runes", which is a symbol representing the nature of a certain thing, such as Fire, Wind, Water, and so on. Runes can be inscribed on objects, which grants the object magical properties, or on people in the form of glowing tattoos (usually on the back of the right or left hand, but on occasion the forehead), which grants the person with the Rune magical properties or the ability to cast spells, depending on the Rune in question. The spellcasting itself is a matter of personal ability, like any skill. Many Runes are unique or otherwise extremely rare, and with difficulty new or more effective versions of old Runes can be created by Runemasters. Runes also are a form of Theurgy in rare cases: aside from the common Runes and rare ones, there are the 27 True Runes, which are both aware and sentient, though usually not very communicative, and in fact most can't communicate at all. Aside from being more potent then regular Runes, True Runes have two side-effects to having them inscribed on a human being: firstly, the subject is immune to the effects aging, though he or she can still be killed. Secondly, each True Rune's "will" is frequently demonstrated by forcing the character (most often the hero and lead antagonist) along certain paths of fate, as each True Rune has a complicated destiny associated with it.
In Magicka a steam game there is an elemental rule based magic system. You summon 8 different elements that combine with each other in different ways to create new deadly effects. Some deadly to yourself as well. For instance summoning lightning elements while wet hurts the player. Combining rock and fire though yields a fireball, while combining water and fire yields steam, etc. There are hundreds of combinations.
In Dragon Age magic has several flavors. Mages (one of selectable player classes) is a mix of Force Magic and Inherent =Gift. Only people born magi can use magic, and the power of magic comes from The Fade, which is a combination of a Spirit World, a Dream Land, and a Background Magic Field. It's possible for Mages to use Theurgy to enhance their own powers and even summoning magic with demons but it's dangerous because it can cause Demonic Possession. Even good spirits can create Well Intentioned Extremists. Dwarves are stuck with inherent Anti-Magic so instead they use game's highly toxic resident Green Rocks lyrium to craft magic weapons (include laser beam staffs) and even a big Magitek ball that accidentally shifted them into another dimension filled with demons giving them Device Magic, they may also possess Alchemy assuming they invented the skin salves that can stop lightning bolts. Bards can apparently use Magic Music or they're just really good at singing. There's even a Magic from Technology example with the Templars who get Anti-Magic and Smite Evil by drinking lyrium, too bad it eventually turns them into crack-heads.
In Sabres Of Infinity, magic takes the form of the Bane. the Bane is a magical force that exists in all living creatures, but only those with a considerable potency in their blood (known as Banecasters) can use it to manipulate their surroundings.
Magic in The Elder Scrolls is a mix of Rule, Force, and to some extent (with all the magical artifacts) Device magic. Gameplay-wise, it is simply Rule magic, but taking the "lore" in account, the different magic schools become nothing but labels the Mage's Guild puts on the different effects the use of magic has. Apart from Alchemy there is no limit at all to magic, and many cultures have created their own kind of magic "styles" which don't fit in with the Imperial Schools at all.
Skyrim retcons the Thu'um as draconic Force Magic. By speaking words in the dragon tongue, a Thu'um wielder can alter reality itself. Crosses over with Divine Magic, since these "dragons" are Aedric.
Eternal Darkness uses a combination of Rule Magic and Theurgy; spells are set up almost grammatically, but require one of four Eldritch Abominations to lend their power alignment to the spell. Some characters occasionally have prepackaged Device Magic that lets them cast various spells a limited number of times, at least until they gain access to the Tome of Eldritch Lore that lets them cast spells on their own.
In the Exile and Avernum cRPG series, magic is pretty much everything but Wild Magic. Both arcane and divine magic is present, but the energy required to cast spells is the same for both. There don't appear to be any Ley Lines or somesuch, so the source of mana is somewhat unclear. Just about anyone can learn magic, but learning is not cheap, and likely also heavily restricted via legal means. Both divine and arcane casters can summon creatures to do their bidding, divists mostly spirits, and arcanists just about anything but spirits. Alchemy certainly exists, and so does Device Magic. Magical creatures are plentiful (sort of) and possess Inherent Gifts.
Final Fantasy VII has Device Magic in the form of Materia (sort of like processed life force), as well as Inherent Gifts, though other forms of magic seen in the game are markedly less Functional. If you believe the theory that most of the Final Fantasy games are connected to each other in at least some small way, all magic in the series seems to originate from the Elemental Crystals and Summon Spirits (both forms of sentient Earth Spirits), who like to essentially download information on how to do magic directly into people's brains, which makes nearly all of it a combination of Rule Magic and Theurgy.
Final Fantasy VIII uses a combination of Theurgy in the form of Guardian Forces and Force Magic in the form of para-magic, the ability to do such sometimes being granted by Guardian Forces. Sorceresses use magic that resembles the Inherent Gift, but the methodology in which they use this magic is what para-magic is based on. Though Guardian Forces are used to allow SeeDs to use para-magic, they are not required, as most Galbadian and Estharian soldiers can use it without GF assistance.
Final Fantasy XII uses Force Magic, the Mist is the source of all magic, and when concentrated into nethicite, it starts to act like plutonium gone beyond the critical mass.
Final Fantasy I notably featured rare (for this series) examples of straightforward Device Magic, as several items could be used to cast spells even by classes prohibited the use of natural magic. However, most of the game stayed true to a Dungeons & Dragons style magic.
The Myst universe uses Rule Magic. Write in the right language with the right ink in books made with the right sort of paper and the book will become a portal to the universe described in the book. Opinions differ as to whether this creates the universe or merely links to a pre-existing one, and whether "be of the right bloodline" is also in the conditions.
Typically only the insane believe the Art actually creates worlds, and Anna/Ti'ana and Katran/Catherine disprove the latter. Also, the Bahro have the ability to Link as an innate gift, and Yeesha can break the rules and do pretty much whatever the hell she wants in her ages.
Anna and Catherine disproved the former as well, being from Earth and Riven respectively as opposed to D'ni descent. Catherine also displayed a talent for bending the rules to their breaking point; it's possible Yeesha's gift is merely an extension of this explaining why her belief that she was the Messiah ultimately doomed her attempt to free the Bahro in Myst V: End of Ages.
Alchemy — The folks at Atlas, although it's a bit more complicated than mixing potions or making magic items. They "create the future, using the ingredients of the present." Basically an organization of Chessmasters who use The Plan to do everything. They can do this because they organize their brains into supercomputers. A more classic version is part of the Einzbern magecraft, for instance, taking a silver wire and then using magic to form it into an eagle to attack one's enemies.
(limited) Device Magic — Mystic Codes (the "wands", so to speak), Conceptual Armaments, Knight Arms
Elemental Magic — Although different from the classic ones. The element of a magus is determined by their Origin. Whatever that Origin is, the magus is more likely to specialize in it.
Force Magic — Powered by Ley Lines or similar mana pools, which are natural places to manipulate Mana.
(limited) Inherent Gift — Humans need at least the Magic Circuit to use magecraft, and individuals born with a higher number of (or better) Circuits will have an inherent advantage. There are also Mystic Eyes, a form of Magic Circuits inherent to the eyes, the most powerful of which are the Mystic Eyes ofDeath Perception, which allow the user to "see" death as a concept and be able to fully realize it.
Mentalism — Includes psychic powers (under Mystic Eyes) and Reality Marbles (close to Sorcery).
Rule Magic — The "theory engraved onto the World". The magecraft also applies Equivalent Exchange, although it's not as obvious. Mana is a requirement to perform magecraft. Although, some techniques can be used to reduce the cost of mana in performing magecraft like Shirou's case; his mana cost for Gradation Air is practically zero within Unlimited Blade Works.
(limited) Wild Magic — The Counter Force. Of course, then you have the thing called Magic or Sorcery, which is defined as "the impossible."
An expansion pack for The Sims 2 introduced this. It's mostly Rule Magic, all spells require items called reagents that can either be bought, or made in a cauldron for free, albeit time consuming. Benevolent spells typically have reagents described to be from a good source, such as crystallized moonbeams, and dragon scales willingly given up by an elder dragon. Malevolent spells require reagents described to be gotten from causing harm, such as snake venom painfully taken from a snake, and literal Eye of Newt. Also you have to be a member of the Witch Species, which you can convert to.
Tales of Vesperia uses a bit of Force Magic and Device Magic together: to perform magic, one must use a Blastia to weave the Aer around them into a spell to use. The exceptions to this are the Children of the Full Moon. They have no need for blastia and tend to be extremely powerful.
The Ultima series uses Rule Magic except for Ultima VIII which shoehorns in every single style, and forces your character to learn all of them in order to complete the plot.
The Warcraft series uses pretty much all of the variants. (In story terms, at least. In terms of game mechanics, every class with any magical ability uses Force Magic — magic powered by mana in most cases, or in the case of death knights, runes charged with magic that can be spent on a spell and periodically recharge on their own.)
Mages use Arcane Magic, a combination of Rule magic and Force magic. It relies on drawing power from the Twisting Nether, and magic energy tends to flow along ley lines.
Warlocks use a combination of Arcane magic and Theurgy (dealing with demons).
Shamans use a third type of Theurgy, drawing their power from communion with the elemental spirits — this is much more pronounced in the novels, where they have to go so far as to ask the spirits for each individual favor.
Druids use Wild Magic from the Emerald Dream, the living blueprint of a wild world to which Azeroth would revert without civilization.
Priests are sort of glorified psychiatrists, redirecting the forces within the collective consciousness of their species for healing, enhancement, protection, and blowing up people's minds and/or melting their faces.
Death Knights' powers seem to come from within their own altered natures. It's actually a combination of talents gained from undeath and an understanding of runic magic, which essentially involves replication of ley-line patterns on a small scale in order to produce effects — so, Force Magic's involved in the lore, too, with a bit of Rule Magic involved since each sort of rune (is supposed to) create only one kind of effect.
There's also a wide variety of magic items for Device Magic. Any piece of gear that increases your stats can essentially be considered Device Magic (apparently your character's Strength/Intelligence/Agility/whatever is augmented simply by equipping the item), and these can be disenchanted into reagents used for enchanting other pieces of gear.
The Ar tonelico games use Magic from Technology which in practical terms functions through a combination of Rule Magic and Inherent Gift. Magic power derives from a series of towers built by an ancient civilization and can only be accessed by so-called Reyvateils, who are the beings that administer the towers or those descended from them. Spells are cast through songs, sung in a language called "Hymnos", which function like computer programs that interface with the tower with which the caster is affiliated to summon forth magic.
Doom III managed to have one Device Magic weapon in a world where teleportation into hell had become a possibility through technology. The Soul Cube could not be analysed due to its immunity to radiological scans (making it impossible to determine its atomic makeup), was sentient, had a constant body temperature and levitated (making it impossible to calculate its density). Its creation involved sacrificing the Martian race.
In Might and Magic VIII, there are three races (which function as classes in that game) with inherent racial abilities.
The Persona series delves into magic quite a bit, and Persona 3 works especially hard, via the school nurse Edogawa's magical theory lessons, to establish a consistent, reality-based magic system. Essentially, Persona summoning could be considered a form of Theurgy, with the Personas themselves utilizing Elemental Powers. Fuuka and Mitsuru are also capable of a limited form of Divination.
Theurgy and Device Magic: Humans in most games must rely on machinery to perceive, negotiate with, and summon "demons" to perform magic for them. Negotiation is important, because demons have multiple factions, and siding with one means a tougher negotiation with others.
Alchemy: The Demon Fusion mechanic, which treats demons as components by which you can produce new demons, and thus, new magic.
Touhou's Spellcard system is notable because of how it deals with Rule Magic; the rules are basically a self-imposed consensus agreement, in order to ensure everyone has an equal footing in magical duels. Most characters in the game fall under Inherent Gift, complete with Superpower Lottery. However, Theurgy is used in several notable instances, such as summoning the powers of gods, and several characters display some form of Device Magic.
While the details of how a magic-wielding City of HeroesPlayer Character operates are limited only by the player's imagination, the description of the Magic origin in the character creator specifically mentions three types; those who wield magical artifacts (Device Magic), those who study and cast spells (Rule Magic), and those who have made pacts with mystical entities (Theurgy). And that's not even getting into the other four selectable origins (Science, Technology, Mutation, and Natural), or Incarnate powers available to all top-level characters (which would fall somewhere between Theurgy and Wild Magic).
King's Quest: These type of spells are all Alexander seems to be able to cast. Not that he can't be terribly inventive with it.
.hack is supposed to be a game within a game, so obviously, the "real world" has no clear example of magic. There are some things that advanced programmers can do that are reminiscent of magic, but that's debatable. The "game world" uses Rule Magic, unsurprisingly. What little there is of the background story suggests that Wild Magic is also at play.
The Secret World features many different varieties of functional magic used throughout the game by either the player character or the NPCs.
Theurgy: A variation- because they have been symbiotically bonded with one of the AgarthanBees, players have the ability to wield magic, either casting traditional spells or channeling energy through their weaponry.
Inherent Gift: Many characters were simply born with magical powers, in some cases because of genetic inheritance, in others for no percievable reason at all.
Rule Magic: Secret Worlders who haven't been touched by "The Buzzing" and don't possess inherent gifts have to learn how to use magic through incantations, gestures and rituals. Though it works as good as the other two variety, it takes a long and risky education process to master- though some people find it easier than others- Hayden Montag was casting advanced spells before he hit adolescence, while John Wolf had to study for thirty years just to cast a simple fireball spell.
Device Magic: The Illuminati have taken this to an artform in crafting various Magitek objects to control or enhance magical processes: Lore entries mention imprisoning demons inside specially-made hard drives, Dr Zurn provides a full-body workout for your powers and a flashback to the Tokyo incident with a simple injection, and the faculty at Innsmouth Academy reinforce their wards with W.A.N.D. anima devices.
The Witch's House: Subsequent playthroughs after getting the True Ending reveal that Ellen couldn't cure herself; someone else had to take her place, as well as the fact that Witches' powers are granted to them by demons (in this case, the talking cat) in exchange for souls to devour, making the game's magic theurgy, with Equivalent Exchange.
Final Fantasy X: While normal magic (i.e. Lulu's elemental spells and Yuna's white magic) isn't explained to be governed by any real rules, the abilities of a summoner are said to be and Inherent Gift, as when Wakka first talks about Yuna, he says she "Had the talent", implying only some people have what it takes to bond with the Fayth and summon Aeons.
Final Fantasy X-2: The Garment Grid system is a form of Device Magic, allowing the girls to access the abilities of the person whose memories are held within the sphere (e.g. Lenne, a popular performer in ancient Zanarkand, is the one whose memories make up the Songstress Dressphere); the magic the girls gain access to from the spheres comes in virtually all flavors, (Black Mage covers Elemental Magic, Songstress uses Magic Music, the Beastmaster uses Summon Magic, etc) making it very versatile overall.
Chrono Trigger: The magic learnt by the main cast (sans Robo and Ayla) is a hereditary Inherent Gift; it just takes a visit to Spekkio to unlock it. Robo is a robot, so he can't inherit the 'spark', as Spekkio calls it, and it's later revealed that only after Lavos fell and began influencing the progression of the planet did people begin to develop powers. Ayla was born before this, so she doesn't have the gift (but, oddly, her final attack is a form of Summon Magic), while the other cast members do, because they were all born long after.
In Tower of God, Shinsoo is life, it runs the world, it fuels the world, it shapes the world and it is for all intents and purposes the world. Through Shinsoo, anything is possible, amazing feats, destructive powers even creation of life. The people of the tower live and literally breath Shinsoo, since it makes up their atmosphere instead of air. A powerful Shinsoo user can create something from nothing and turn something into nothing. The use of it can either tear your body apart and kill you, or it can make you immortal. Anything is possible with it.
Most of the magic in The Order of the Stick falls into three categories; Durkon uses Theurgy by praying to Thor, Vaarsuvius uses Rule Magic and the Gates are based on Relic Magic. However, since the webcomic's universe is specifically based on Dungeons & Dragons, all of the magical types shown in its entry above will likely apply at some point to a supporting character.
Fey Winds has Force Magic and literal Rule Magic: fey and other creatures of nature (as well as some very rare mortals) tap into "the Song," the force of magic, directly; while humans, elves, and other mortal races must employ "the Rule," a system of formulas and spells. Most of the main cast are also chasing after artifacts (Device Magic) left behind by a strange fey/war golem called Sylphe when she rebelled against those who wanted to use her in a war.
Theurgy seems to be the main magic in the world of The Challenges of Zona with Tula getting her power from the Goddesses of the Moon and Earth while Gruach gets his from Shuach, the evil Fire God. However Mentl uses Magic Music and Vito seems to use Rules Magic, but neither of them is from that world but ours. Shamans have been mentioned but not shown as yet and seem to user a lesser form of Theurgy, than Priests and Priestesses, calling on their tribal totems.
In El Goonish Shive, Nioi is a powerful sorceress, as is Nanase. Nanase in particular uses it very often (although this might just be perception thanks her being a main character) and quite openly at times, and it appears she's subject to Rule Magic. Everybody else it seems has to rely on either a Theurgy pact with an Ancient One to awaken their inner power, which usually result in a Personality Power, Device Magic from either genuine magical artifacts or Magical Alien Machines that seem to focus Baleful Polymorph abilities (at least of the ones we've seen), or be lucky enough to have been genetically engineered for magic from birth. And that's not even focusing on some elements of magic that are only just being introduced, let alone explained.
Additionally, all magic seems to run off of Wild Magic, in that sometimes magic has unexpected, but usually harmless side effects. It's even been stated that magic has a 'flair for the dramatic'.
Sluggy Freelance has two kinds of spellcasters: there are the ones who are parodies of Harry Potter characters, who use a combination of Inherent Gift and Rules magic (they have to go to school to learn how to cast spells, but if you don't have the knack for it no amount of schooling will help you), and then there's magic cast using the Book of E-Ville. The Book contains a number of Theurgy spells, but it also seems to have a will of its own and has granted Gwynn an array of magical abilities, making it cross between Device Magic and Wild Magic. Of course, this is just human spellcasters; there a number of magical beings in the Sluggy verse that are too diverse to get into here.
This is a crucial element of the world in Unsounded. Magic is so commonplace it's not even called "magic", because that word implies something mystical or unknown — instead, it's called "pymary". Specifically, it's Rule Magic, controlled by speaking a Language of Magic. It is actually extremely structured and orderly, with many rules that must be strictly adhered to — Word of God has compared it to computer programming.
Blindsprings has "Academic Magic". While specifics have yet to be given, it appears to be some form of Rule Magic, perhaps with elements of Device Magic (as seen in the rune-inscribed cards or pages that Harris uses to cast his spells). Alchemy has also been mentioned.
In True Villains the magic seems to be made up of some weird mix of Inherent Magic which Mia possesses, Alchemy which Sebastian uses, and then one of the other types for the rest of it- possibly Theurgy, as Bayn goes to see his god, Ket, to restore his power after he loses it. However, Sindal was noted to "study" wizardry, so maybe Rule Magic too? Maybe all of them.
The Whateley Universe has several of these forms. It's Rule Magic, but with Theurgy and Force Magic (ley lines are a popular energy source for mages like Fey) and Alchemy and Device Magic as features of the Rule Magic. Some of the classes listed above are done by mutants instead of mages, although in Winter Term there is a special topics class called 'Necromancy: Threat or Menace'. Apparently, last winter term there was the same magical special topics class, but it was on theurgy.
Chatoyant College has various kinds of magic in the story but it is clear in the lessons, and hinted at in the story for the other kinds, that there are strict rules to how it is applied:
Inherent Magic: This is magic that comes from within a person. It depends on the magical abilities of the person concerned and it broadly follows the 4 elements: earth, air, water and fire.
Trance Magic: This is when someone utilizes the magic in the stuff around them. One needs to go into a trance to access it and it is more flexible.
Deucalion Chronicles features most types of magic, but all of it is, at the most basic level, Force Magic drawing on the framework of reality, Afflatus.
Magic in Chaos Fighters is slightly complicated. The system as a whole is rule magic and elemental magic. However, formation spells is more heavy on rule magic than free form spells. Then, there's magical skills which is physical attacks powered up with aura. Weapons charged with aura when stabbed onto the ground produces wild magic, which is a type of magical skill.
Every single form of magic exists in the Global Guardians PBEM Universe. Practitioners of magic are on both sides of the "hero/villain" moral line, though there are some who walk straight down the middle of the line. The most powerful wizard on Earth is the Warlock, also called The Archmage.
In Trinton Chronicles it seems like along with super powers magic exists and is used for everday chores from cleaning up tables to moving heavey or otherwise hard to move objects with ease.
Mage Life All living creatures in Mage Life is born with some form of an inherent magical ability. Some may even cultivate it and make it grow.
Linkara's magic gun
Almost all the magic used on Kim Possible is device-based, mostly in the form of monkey-themed ancient relics discovered by archaeologist/freak Monkey Fist. However, at least one character has been seen using magic powers without the aid of a device.
Avatar: The Last Airbender makes copious use of Inherent Gifts in the form of Elemental Magic, though it appears to not be genetic and anyone is born with the chance of becoming a bender. Aang, the Avatar, is the only one that can do this for more than one element, as well as having Force Magic and functionality as a medium from the Avatar Spirit.
Each element requires a different, and largely incompatible, approach to control. While Uncle Iroh is shown to use a Firebending technique inspired by the principles of Waterbending to deflect a Lightning strike from Azula., it is said that even this takes a lot of spiritual flexibility. Actually bending two different elements would be unthinkable.
Also, bending itself is said to be originated from people copying the moves of either Badgermoles (Earthbending), Dragons (Firebending), the Sky Bisons (Airbending), or the moon (Waterbending). It was shown that waterbending and firebending can change depending on the visibility of the moon or sun respectively. That and statements by the creators suggest that the abilities are affected by nature, which is likely the source of their powers, also making all bending a form of Force Magic (the connection of the moon and ocean spirits to their elements may make it technically Theurgy).
Bending isn't the only form of 'magic' implied in the show, though. One episode revolves around a gifted, very accurate fortune teller, whose abilities are not explained.
There are also the spirits, whose abilities aren't clearly defined (and probably vary a lot from spirit to spirit), and may be the ultimate source of bending. Interestingly, the spirits are the only entities in the show whose powers are generally referred to as "magic".
It's also mentioned by Guru Pathik that the distinctions between elements are an illusion, and the Lion-Turtle implies that element-bending derived from bending the energy within oneself, implying that the whole thing is Force Magic that just behaves like Elemental Powers because the users have spent so long treating it that way.
The creators have also gone on record as saying that they wanted to create the series with a magic system that has an inherently physical component to invoking it, hence the elaborate stances and moves used by various benders. How "good" a given bender is at their area of bending depends on how well they can make those moves, and getting better at bending involves lots of necessary physical training and practice. Of course, they have also shown with a few exceptional characters across both series, that bending with nothing more than one's mind is possible.
Nearly every one of the above categories showed up in Gargoyles at one point or another, even Wild Magic. "Avalon doesn't send ye where ye want to go—it sends ye where ye need ta be."
According to multiple sources, the Rule Magic of the humans and gargoyles doesn't mix with the Inherit Magic of The Fair Folk, who expressly forbade human magics on Avalon, their home. It should be noted that neither was inherintly superior as Owen/Puck was thrice affected by human magic and could do nothing about it because of this mix.
Jackie Chan Adventures features combinations of rule magic, alchemy, device magic, and force magic. Most of the time the magic is done by Uncle who is the Witch Doctor, but other characters played around with it as well. There's also the talismans, one for every animal in the Chinese zodiac, which classified as Device Magic. Though the talismans were made by stealing a demon's Inherent Gifts (the demons can also provide power for Theurgy, but not used seriously apart from Summon Magic past the first two thirds of season one). Pretty much every kind of magic was used at one time or another by the nonrecurring characters in filler episodes.
The one rule about magic that seems to be hammered in the series is that "Magic must defeat magic".
The Inherent Gift variant appears in My Little Pony: Friendship Is Magic, though this only applies to unicorns. Twilight Sparkle just happens to specialize in magic, so her range of abilities and overall power are far greater than that of other unicorns. It can also be said that pegasi and earth ponies have magic; they just can't directly control it like unicorns can. According to Word of God, earth ponies bless the land and tend to be better with animals and whatnot. (Fluttershy is an abnormality) It would also certainly explain other abilities the non-unicorns have expressed, such as the Pinkie Sense, Fluttershy's stare, and so on.
Aladdin has Jafar, who at first has access to Alchemy and Device Magic (the staff, which loses its power when broken - the Magic Carpet is another example of a Device), and the Genie, who being a supernatural creature counts as a Theurge. When Jafar has the Genie turn him into "the most powerful sorcerer in the world", he has more powerful Innate Gift powers of transmutation and the like, but he's still less powerful than the Genie, until he wishes to be a genie himself (albeit "an all-powerful" one).
In the series, the Genie states the unpredictable dangers of "mixing magic".