Functional Magic - Television Tropes & Idioms

alt title(s): Inherent Gift; Magic

"You can't ask questions, it's magic. It doesn't explain anything, it's magic. You don't know where it comes from, it's magic! That's what I don't like about magic, it does everything by magic!"

— Commander Vimes, Thud!

Any magical system that allows standardized spells that do the same thing every time you cast them. This style of phlebotinum is sometimes subject to its own flavor of technobabble.

Some (but not all) possible flavors of Functional Magic:

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.
Theurgy: where the magic is done entirely by spirits and gods with whom the caster makes deals; the "caster" in this case knows nothing more than a glorified phone number. Wiccan magic — both as practiced in the real world and as depicted in Buffy The Vampire Slayer and, to a lesser extent, Charmed — is mostly Theurgy. When Magic itself is a kind of entity with which casters make bargains and cut deals, this becomes a variety of Wild Magic (below).
- The highest level of this type of magic is Summon Magic, in which the caster summons the entity itself to wherever it is and bosses it around. As one might imagine, this can easily lead to the entity turning on its would-be temporary master if done wrong, especially if the entity is a demon or some other form of Always Chaotic Evil.
Rule Magic: where some underlaying magical rule system is applied, as in manipulation by "True Name" or sympathetic symbolism. Most "study spells and say words of power" magic seen in fantasy literature, films and TV shows are Rule Magic. Real world examples would be Hermeticism, Kabbalah[1], and Onmyodo [2]. Vancian Magic is a completely fictional example.
- 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.
- Magic Music: Another form of rule magic where music is the key to activating it. Used in settings where bards have magical abilities. As one might guess, it is rarely used to be outright offensive and tends to focus more on healing friends and befuddling or beguiling enemies.
Force Magic: Practitioners of magic tap into and control or weave together (by what mechanism is never explained, otherwise it would be science fiction instead of fantasy) one or more magical forces. Magic which waxes and wanes according to how close the manipulator is to a "Ley Line" falls into this category.
Device Magic: Magic performed with some form of mystical device or relic. This is the magic packaged for use by non-casters, along with alchemical potions. Making new devices is sometimes a trade in magic-heavy worlds. Some settings reveal pre-existing artifacts to be Imported Alien Phlebotinum or Lost Technology. See also Magitek, Green Rocks, Green Lantern Ring, Magic From Technology.
Wild Magic: No one has any control over what happens and when, although sometimes it can be influenced. The magic is basically alive. It has its own will and its own agenda and will only help you if it feels like it. Note that a toned-down version of this is basically Magic Realism.

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:

Divination: Seeing the future or the immediately relevant. These are the people who produce the prophecies, though they may also be able to see things far away.
Elemental Magic: The magic users typically work with only one element, which reflects their personality. They might be able to create a volcano with a snap of their fingers but not to levitate a single pebble, or vice versa.
Necromancy: Power over the dead and the undead. Mediums, who can only talk to the dead, get classed with diviners, but those who raise the dead are almost always villains. Still, even then, this is not always Black Magic.
Nature magic: Power over all things living. Quite often includes turning themselves into animals or a Green Thumb.
White Magic: "Holiness." Blessing, healing, protecting... all of the most benevolent of effects. Half of the time includes ways to inflict major pain on deserving targets because Revive Kills Zombie... or at least supposedly deserving targets.
Black Magic: "Unholiness." Cursing, killing, tormenting... all of the nastiest sorts of stuff. Often includes Necromancy as a matter of course.
Equivalent Exchange: Not usually a type of magic, unless the series has "Wish Magic" of a sort. This is when a spell or magical effect requires a sacrifice of equal value to work. This is often a feature of theurgic or wild magic systems, where the books must be balanced for every magical effect performed.

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).

Examples

Anime and Manga

Alchemy, naturally, is the functioning magic of Full Metal Alchemist. Exceptionally talented alchemists are close to, but not quite, Rule Magic users, the only hard-and-fast rule being Equivalent Exchange.
Kido (Demon arts) in Bleach are a form of Rule Magic, anyone can use them if they have spirit power (though some of the incantations sound like Theurgy). All the incantations do is focus it, though you need to be skilled to do a spell without the incantation, and the more powerful the spell the more skill you need. Other races like Hollows use parallel systems that have similar effects of use their special abilities to focus their energy in unique ways.
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 And 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 stated 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.
- There are also the recently introduced sage arts, which combine Force Magic with Rule Magic.
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 X 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.
While Belldandy of Oh 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, tieing 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. Surpisingly, Akamatsu hasn't used elemental-style magic as strongly as most other magic series.
Magical Girl 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.

Comic Books

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.)

Film

The Force in the Star Wars universe is, of course, an example of Force Magic.

Literature

The 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.
Harry Turtledove's Darkness series of books, 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.
Jack L. Chalker's Dancing Gods series combines Theurgy with ludicrously elaborate Rule Magic and takes them to their humorous extreme, resulting in a universe entirely governed by fantasy tropes.
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 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.
The "warrens" and "wards" in the Malazan Book Of The Fallen are examples of Force Magic.
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 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).
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 with their mind (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).
Magic in The Bartimaeus Trilogy 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.
The book and movie The Last Unicorn use entirely wild magic. Magic only seems to work correctly when it advances the plot. Schmendrick even frequently gets important things to happen by repeating "Magic, do as you will."
- Although it's worth noting that having the power but no real control over it is precisely Schmendrick's personal bugbear, to the point where his former mentor gave him a form of immortality just so he might live long enough to finally get a grip on his magic. The actual form of magic he tries to use seems to be primarily Rule Magic, while magical creatures like the titular unicorn have their Inherent Gifts.
The 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.
The Chronicles of Thomas Covenant by Stephen Donaldson uses a combination of Rule Magic, Force Magic, Device Magic, and Alchemy. At least, until the titular Thomas Covenant comes along, with his white magic ring — by which he can liberate the Wild Magic. Now, if only he could control it and use it...
The Enchanted Forest Chronicles by Patricia Wrede uses almost all of the above.
- 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.
- 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 Shannara series is one of the few true aversions this troper has seen - the books go out of their way to describe how magic resists being nailed down like this, and the magic of the series is constantly evolving.
The "Klatha" of James Schmitz's Witches of Karres would qualify as "Force Magic" though the Witches themselves have made up strict rules regarding its use.
The wizards of the 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.
As stated above, Force Magic, when explained in detail, can sometimes shade into Science Fiction. If, for instance, a space traveler from a high-tech culture lands on a planet with "magic" that turns out to have a scientific justification (or more commonly a Hollywood Science justification), then it's usually revealed to be either Magic From Technology or Psychic Powers. The Warlock In Spite Of Himself and The Cyborg and the Sorcerers both use this premise.
In Mercedes Lackey's Heralds Of Valdemar series, the idea of treating magic as a scientific endeavor, with predictable rules and outcomes, caused serious distress on the part of one of the mages...especially when it turned out to work.
- Actually, dear Myste has a variety of magic systems working for her. The Velgarth (aka Valdemar) series alone shows instances of Inherent (in the 'mind-magic' Gifts of the Heralds, as well as the inborn capability to perform magic for the rest of her mages), Theurgy (Both with the Shin'a'in Shamans and the Karsite Priests, as well as her northern 'barbaran' tribes), Rule Magic (traces show up in most of the magic sytems 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 is this), and White and Black Magic (the Vkandis Priests and any of the magical Big Bads respectivly, especially the Blood-path mages.)
- In her lesser-known Elemental Masters series, we see blatant Elemental Magic, combined with aspects of Nature Magic (particularly for Earth mages), Force Magic, and Theurgy.
  - Her 500 Kingdoms series also has a variety of magics. Champions tend to make use of magical objects a la Device magic, Witches and Hedgewizards are mostly Nature/White magic, while Wizards and Sorcerors (and their female counterparts) are more Rule/Theurgy magic. Almost all of her magic characters in any of her series (notable exceptions being Madame Arachne and her son Reginald of the Elemental Masters book 'Gates of Sleep) have an inherent gift for magic, so does that make all of it Inherent magic too?
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 Spellsinger series by Alan Dean Foster has the titular superpowered bards as the most powerful magic-workers. It's a combination of Inherent Gift (you have to have the gift) and rule magic (and 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.
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.
Magic in 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.

Live Action TV

Charmed uses Theurgy and Alchemy for all wiccans. Most true witches also get Inherent Gifts.
Buffy The Vampire Slayer has shown all of these, although Wild Magic was far more rare than all the other varieties.
Out Of This World uses Rule Magic for gleeping and Inherent Gifts for Evie's other powers.
Power Rangers Mystic Force is technically Rule Magic mixed with a magic-users-only version of Device Magic (the Ranger's Morpher-wand-phones), though "spell codes" outside the core ten spell words sometimes had effects that were, to be charitable, not quite what might have been expected (the one-word code "finishio" was particularly guilty of this) and Inherent Gift magic (their elemental attacks, activated simply by believing in them.)
- Furthermore, many Power Ranger teams are powered by Device Magic, (eg., 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 Morphin' Grid.

Tabletop Games

Speaking of Dungeons And Dragons:
- 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.
Role-playing game example: As of the new World Of Darkness, vampires use Inherent Gifts, mages use Force Magic laced with Rule Magic (and by a different set of rules than the mages of the old World of Darkness), Prometheans (think Frankensteins Monster) use an odd version of Inherent Gifts derived from Alchemy, and changelings practice a form of Theurgy based on deals their masters made with primal forces. 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.
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).
The equivalent to magic in Warhammer 40000 can loosely be described as a combination of Wild Magic and Theurgy. Only replace "Wild" with "Cosmic Horror".
Mage:The Awakening of the World Of Darkness TRPG combines most of these in the form of the ten Arcana. Basically, given enough mana and enough skill in the necessary Arcanum or Arcana, you can do pretty much whatever you want. That is, unless there's a human around, in which case you have to worry about Paradox...
- In the Second Sight supplement book, various forms of lesser kinds of magic are also mentioned, including Alchemy, Psychic powers, and a Cosmic Horror 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 Horror magic list.
In Deadlands, 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 done by playing poker with the manitous. 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.

Video Games

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 eachother 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.
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.
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.
It is easier to say that 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 the Avernum (Exile) 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 - mana. 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.
The Magecraft in Nasuverse contains:
- (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.
- Theurgy — Epic Spirits, Elementals, et al.
- Rule Magic — The "theory engraved onto the World".
- Alchemy — The folks at Atlas.
- Force Magic — Leylines, which are natural places to manipulate Mana.
- (limited) Device Magic — Mystic Codes (the "wands", so to speak), Conceptual Armaments, Knight Arms...
- (limited) Wild Magic — The Counter Force.
  - Of course, then you have the thing called Magic, which is defined as "the impossible" (Operation of parallel worlds, denial of nothingness, etc...)
The Warcraft series uses pretty much all of the variants. Arcane Magic (the "usual" magic) is 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). Demonic magic throws Theurgy into the mix (dealing with demons). Priests and the like use Theurgy (their magic is powered by faith in whatever force they believe in), while Shamanism and Druidism use Wild Magic. There's also a wide variety of magic items for Device Magic.

Web Comics

Gunnerkrigg Court uses Inherent Gift magic to explain Antimony's and Surma's talent as mediums and Zimmy and Gamma's various telepathic abilities. The Blinker Stones are Device Magic. Ysengrin's "terrifying skills of gardening" border on Theurgy, as they were given to him by Coyote (but he uses them like an Inherent Gift). Symbols from Alchemy appear frequently, but their significance is unclear. And the Donlans' magic is completely unexplained, but considering the highly geometric patterns and the nature of the feud between the Court and the Wood, it can be suspected to be Rule Magic.
Most of the magic in 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.

Web Original

Homestar Runner plays on this in the Strong Bad eMail "shapeshifter", where he sarcastically notes how lame shapeshifting powers get when rules and limits are tacked on:
Strong Bad: (in sarcastic tone) You can turn into a machine gun but not bullets. Contemporary jazz turns you back. You can only turn into things your grandma's knitted you. Crap like that!
All of the above styles have been shown in the Whateley Universe. Different wizards and mages and magical practitioners use different styles. The main character Fey has innate magical gifts, as well as the ability to tap into Ley Lines, plus she's in training to learn lots more (she's a high schooler). This is due to her being the magic of an ancient Sidhe Queen who has 'combined' with her. As a result, she now looks like said Sidhe too.

Western Animation

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 effected 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).
Nearly every one of the above categories showed up in Gargoyles at one point or another, except possibly Wild Magic.
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.