Hermeticism is a real-world philosophical, religious, and magical tradition, ascribed to "Hermes Trismegistus", the Coptic Egyptian gnostic who founded the theological and philosophical base of western alchemy. Fictional depictions of European, Armenian, and Islamic alchemy will usually represent it as Hermetic.
Hermetic magic is quite time consuming, since each and every spell needs to be researched and planned in advance. The actual casting of a spell also takes a lot of time too, since it involves a lot of props, drawing of diagrams, and suchlike.
These days, Hermetic magic is used more in anime than Western works, partly because it gives a Japanese work a European flair, and partly because Western authors are unwilling to spend pages or screen time on it. (Westerners seem to prefer using systems that allow for quick casting of previously-prepared spells.)
Expect to see The Seal of Solomon, the Qabbalah, Tarot cards, and the Enochian alphabet in works featuring Hermetic magic (the Paracelsian Alphabet of the Magi, less known by name, is nevertheless also likely to make an appearance).
See Instant Runes, Magic Is Mental, and Fantastic Science. Compare Ritual Magic.
Lampshaded in one episode, part of the reason spell names are recited is to warn folks that the Goddesses are casting it. In fact, outside of the more complex spells that require multiple casters and/or spell circles, they can cast most things instantly.
Spellcasting in Slayers is somewhere between Hermetic and Vancian models. The basic combat spellcasting is based on Vancian-type spells, but many mages use longer Hermetic rituals with magic circles and stuff (most often these are used for summoning demons and enchanting items).
Furthered when a zoom out reveals the entire city of Seyruun is built in the shape of a gigantic magic circle—made so in order to weaken any black magic used within the city's walls.
Alchemy in Fullmetal Alchemist requires a circle for any transmutation to occur. The formula within said circle defines how the gathered energy is channeled.
Even with Edward Elric and others transmute by clapping their hands, it's explained that the requisite circle is represented by the ring formed by the alchemist's arms when they 'clap'. The big sign that Hoenheim and Father are truly abnormal is the fact that they don't even need to do that.
Much of Yu-Gi-Oh! (primarily the first series) deals with ancient Egyptian magic. During the Doma arc, Dartz, the Big Bad for that part of the series, uses a unicursal hexagram called the "Seal of Orichalcos", which is seen inside a circle with the Enochian alphabet spelling "Oreichalkos" twice in the border.
Unfortunately, in the Japanese version of the anime, the runes on the Orichalcos cards do not translate into actual words (a subverted Bilingual Bonus).
Hellsing, Fullmetal Alchemist, Trinity Blood etc. have a mini-trope of printing magic symbols on the back of the hand on the white gloves the characters wear. This appears to be a visual shorthand for "western magic user".
In FMA, at least, the symbols are the magic, in the sense that they're a necessary conduit controlled by the user to manipulate energy and matter. It works with tattoos as well.
Symbols of some sort light up on Mikoto's sword Miroku in Mai-HiME.
Cardcaptor Sakura's titular character has a magic seal that materializes whenever she uses her Clow (and later Sakura) Cards. Note that the creator of the cards, Clow Reed, was not Japanese but half-Chinese, half-English. Part of his unusual power came from having access to both Chinese Taoist and English Tarot magic.
X1999 utilizes a lot of European mystical symbolism, including Tarot and Qabbalah, but four of the seven protagonists derive their powers from traditional Japanese sources, including practical Buddhist magic, Shinto deities, and Taoism-based onmyoujitsu.
The magic system in Magical Girl Lyrical Nanoha, whose spells are always accompanied by Instant Runes, and whose really impressive spells either get really big magic circles or multiple ones, with the occasional long chant.
Addie and Honami from Rental Magica both use this kind of magic, with Addie utilizing Goetia and Honami using some Celtic magic that evokes the descriptions given by Pliny the Elder.
Bleach falls somewhere between this and Vancian Magic in regards to Kido. Shinigami need to spend a rather significant time learning the incantations for the various types of kido used, and each one has a specific use. Also, the full name - if not the entirety of the incantation - has to be used by lower-ranked shinigami if it's to be effective; a standard "holy crap that guy's strong" reaction follows a Lieutenant, Captain, or Big Bad spitting out no more than the number and it being more powerful than any other use seen to date. That said, if one such being is doing a full recitation? Run.Unless you've just won a game of one-upsmanship with them and now basically transcend everything but the gods themselves, for a few minutes anyway.
Subverted in any Kido spell it depends on how long you spend training that spell. A low-level spell offensive spell can be potentially deadly. Like when Byakuya uses a level four Hado spell for a cheap shot at Ichigo that went through his shoulderlike a laser. Shown from a distance shot, it went about 50 meters. Where as when Aizen used level 90 offensive spell without an incantation, it just knocked out Sajin from Standard Bleeding Spot wounds. The very same spell with full incantation could allegedly warp the fabric of reality as its full "strength" is supposedly comparable to the gravity of a small black hole. If you didn't think Ichigo meant business before, him surviving it was a clear indication.
Homura and his followers at the end of the first Saiyuki anime.
Clef, Zagato, and Ascot use this form of magic in Magic Knight Rayearth. For Clef and Ascot, all magic that has them summoning creatures uses some sort of circular pattern.
Freed's Jutsu Shiki seems to be this in Fairy Tail. It may very well be the most broken type of magic in the whole series as Freed can make any kind of rule he wants with it (he traps people within invisible barriers and the rules are such as "no one over the age of 80 can get out" or "all oxygen in this room will be depleted"), but it takes a very long time to set up (it isn't known exactly how he does it), so he has only used it effectively in one arc.
Promethea is in essence what would happen if Wonder Woman decided to devote her comic book to an explanation of Western magical traditions, including Hermetic Magic and Kabbalah. It's written by Alan Moore, a real-life practitioner, so it's to be expected
Harmony Theory: As a pegasus, Star Fall has no horn and so casts spels by drawing magic circles on spell paper.
Katherine Kurtz's Deryni series features elaborate ritual magic workings for everything from scrying to bestowing magical powers.
John Bellairs's novels often featured Gnostic magic, with direct references to the Keys of Solomon in The Letter, The Witch, and The Ring.
Thaumathurgy (ritual magic) from the The Dresden Files follows most rules of Hermetic Magic: It requires a magic circle and some rituals and ingredients to work, and must usually be set up with a little planning. Thaumathurgy is described as the 'scalpel' of magic in comparison to the 'hammer' of Evocation, which is just calling up an element to produce a quick, crude (but instant) effect on the fly.
Demon-summoning in The Bartimaeus Trilogy is extremely complicated, primarily involving magical circles and knowing the name of the demon, but also knowing dozens of other languages, candles, incenses, not leaving the circle until you are sure the demon won't hurt you, knowing how to play various music instruments well, among other things. And that's just the basics, as demon summoning just becomes more complex from there.
Note that, in this universe, anyone can theoretically do magic; the main reason there's a separation between magicians and Muggles is because, in order to learn magic, you basically have to pass a test as a child saying you have genius intelligence, 'cause otherwise you'll probably blow yourself up.
Parodied in Discworld, where magic doesn't work like this, but wizards often act as though it does because it looks impressive. The Rite of Ashk-Ente is the classic example: It can be cast by a single powerful wizard with three bits of wood and a fresh egg, but if you don't have eight archmages chanting at the corners of an octagram filled with occult paraphenalia, you aren't doing it properly.
Some elements of Harry Potter's magic are hermetic. The most notable instance is probably the resurrection of Voldemort in Goblet of Fire.
Miles Cameron's The Red Knight
Truth in Television: There are a number of groups still practicing Hermeticism, despite many occultists going over to the less intense/time consuming Chaos Magic and Wicca-influenced stuff. Aleister Crowley, the Ordo Templi Orientis, and the Rosicrucians fall under this umbrella; two out of the three are still around, and the third was kind of just one guy, so you can excuse him for not living forever.
Forgotten Realms has Eltabbar, a city in Thay "some say named after a demon". It was planned as a huge magical diagram (much like Seyruun in Slayers) sealing Eltab. This was rather precarious, in that if someone draws a really good map of the city, it leaks the seal's power and when it gets destroyed, the seal holding the fiend is weakened a little more. So the Red Wizards had to outlaw mapping of the city under the pretext of security — and did the same with the rest of their land when they're at it.
Thieves' World d20 supplements from Green Ronin use Ritual magic as an alternative — usually the spell's casting time raises by an order of magnitude or so, but so does its duration and gathering enough of mana quickly obviously is less of a problem. Different classes have different affinity to these approaches: mages prefer spellcasting, priests ritualcasting, witches balance them, and Godsworn advance only in ritual magic.
Though previously a bastion of the Vancian system, has changed to include a large chunk of Hermetic magic in 4th edition with the Rituals system.
Ars Magica literally uses Hermetic Magic— in this case, a unified magic theory created by a master magus named Bonisagus, whose apprentice Trianoma founded the Order of Hermes. Somewhat different from the trope's definition, as Kabbalah and similar traditions are not included in Bonisagus' theory, but still includes rituals, time-consuming spellcasting and the like.
Similarly, Vampire: The Masquerade have the Tremere clan, who used to be House Tremere from Ars Magica until they realized that magic was fading, and with it, the immortality they'd purchased through alchemy. So, they corraled a bunch of vampires, forced them to Embrace, and got a new kind of immortality. They practice potent blood sorcery, but it's ultimately a bastardized version of the magic they practiced while alive. And if that weren't enough, most of vampire kind views them as utter dicks because one of the first things they did after their formation was to ensure the destruction of one of the most decent clans in all of history, and the Order of Hermes's general philosophy for dealing with "the betrayers" is to Kill It with Fire. Ironically, Tremere was trying to legitimize his clan with the destruction of the Salubri; he thought if he could diablerize Saulot and claim his power, he could get a foothold in vampiric society. However, Tremere's entire life can be summed up with "It half-worked"...
The Star Ocean games have Heraldry/Symbology/Runology, which involves etching symbols, on nearby surfaces or on the caster themselves, which can then be used to create spells. It is revealed in Star Ocean: Till the End of Time that the symbols are in fact parts of programming code for the virtual universe the characters live in, and allow them to warp reality. It Makes Sense in Context.
One should also note that: It still works when the main character uses his (and his love interest's and cousin's) literal gamebreaking code to open a portal to the 4th dimension, that is, the real world, where they are part of a video game.
High Magic in Lusternia is hermetic. It's basically a very well-researched ode to Qabbalah - each spell references an aspect of the Sephirot. It's diametrically opposed to the more illogical, intuitive branch known as Low Magic.
Where other Real Time Strategy games have buildings and other structures, Grim Grimoire has Lillet inscribing various magic circles from which she summons demons, ghosts, and other units to overwhelm her enemy with.
In general RTS have hints of it if they have a middle age theme and require certain buildings to cast advanced spells.
In Fate/stay night there are many rituals, the most important of which being summoning a Servant (needing various ingredients and a specific formula) and the Holy Grail War (the battle between the seven Servants, until their souls fill the system and allow to summon an all-powerful wish-granting machine. At least in theory).
The 'mindslave' spell Hekate uses in the Whateley Universe story "Christmas Elves". For that matter, humans with the time and inclination can learn and practice this style of magic without necessarily requiring innate superpowers in this universe; Wizard-class mutants just have a natural knack (and may, at higher levels, be able to work more comic-book style spontaneous magic as well).
Adylheim has low magic which fits this trope to a tee, although the precise mechanics of casting are generally skipped over.
In Gargoyles, human magic requires intensive study, even if the actual incantation is only a simple phrase. However, once the requisit spell and gestures are memorized you're usually good to go unless you need ingrediants. Magic of the Third Race however averts this intirely. They just speak a little rhyme and they're good.
Anime and Manga
InuYasha is chock-full of traditional Japanese magic (and monsters). Also Rumiko Takahashi's earlier Urusei Yatsura, despite being nominally science fiction.
In Fate/stay night and Fate/Zero, the two Caster-class Servants: Fate/Zero 's Caster has a magic book that allow him to summon small monsters without the ritual usually necessary (bigger monsters, like Chtulhu (yes, he summoned it too), still need a ritual), while Fate/stay night 's Caster is so good as a mage that allows her to spam spells that would require long rituals, like her trademark Rain of Light (a normal mage would need a magic circle, a ten-count aria and a full minute, or thirty seconds if the mage's very good, to cast a single beam of light, she needs a single word to fire thousands of them).