Fantastic Fighting Style

Martial arts styles that are given a name and/or described in a work of fiction but do not exist in real life.

See also I Know Kung Faux and Supernatural Martial Arts.

Wikipedia's article on this.

Anime and Manga

 * The Hokuto Shinken and Nanto Seiken styles from Fist of the North Star, along with a host of others derived from them.
 * One Piece has a whole bunch of these.
 * Roronoa Zoro uses Santouryuu (Three-Sword Style, one in each hand, one in the mouth).
 * The octopus Fishman Hachi uses Rokutouryuu (Six-Sword Style, with six arms).
 * Many higher ups in the World Government including CP9 use a set of seven techniques called Rokushiki. These techniques include Razor Wind, bullet-like finger jabs, Super Speed, Air Walking, two methods of Won't Work On Meing (one that makes you Made of Iron but unable to move much and one that makes you flexible like paper), and one Ultimate Technique.
 * The number of Fantastic Fighting Styles just go on and on and would take way to long to list them all.
 * Shinmei-ru ("Gods'-Cry School") is the name of a fictional style of kenjutsu used by several manga and anime characters created by Ken Akamatsu.
 * Strike Arts and Kaiser Arts in Magical Girl Lyrical Nanoha Vi Vid are karate-like martial arts that rely on magical energies as much as on the practitioner's fitness.
 * Rurouni Kenshin gives us Hiten Mitsurugi Ryu, a deadly sword style used by Kenshin Himura, the Hitokiri Battousai, focused on blinding speed, reading the opponent's emotions and battoujutsu.
 * From Gunnm (Battle Angel Alita), Panzer Kunst and Ahato Mastarday spring to mind. Not to mention the thousands of sects of space karate, like Tohji's Electromagnetic Karate in Last Order.
 * From Naruto, Killer Bee uses seven swords to attack, without using his hands.
 * Dragon Ball has the Turtle and Crane Schools of Martial Arts, and while animal-named fighting styles exist in the real world, one's where a Kamehame Hadoken is the ultimate move... not so much.
 * Many are shown in Ranma ½: Musabetsu Kakutō Ryū (Anything Goes Martial Arts), Umisenken, Yamisenken, various Martial Arts and Crafts styles, and more.

Comic Books

 * Superman had at least two Kryptonian martial arts styles.
 * Klurkor, which Lois Lane learned in the bottled city of Kandor.
 * The villainess Faora Hu-Ul knew Horo-Kanu.
 * The Green Arrow used Moo-Gi-Gon.

Fan Works

 * The Mega Crossover Undocumented Features has the Asagiri katsujinkenryuu, which combines more traditional martial arts techniques like zanshin with Jedi kata. Special attacks are Hyakken no Arashi and Blade of the Inviolate Soul.
 * Utena Tenjou essentially created her own sword style from nothing, starting with the fencing-influenced Rose Duels of Ohtori Academy, adding in elements of kendo when she becomes the roommate of a kendoka, and eventually learning moves from everyone from Jedi to Klingon warriors to Covenant Elites, until she is skilled enough to simply pick up a lightsaber for the first time and fight with it like an expert. It's only fitting, given that she's one of the central figures of the UF subseries The Symphony of the Sword.
 * Doug Sangnoir of Drunkard's Walk practices a patchwork martial art which he basically built from scratch by incorporating moves he copied from everyone he ever fought in a decade of being a professional superhero. And in the decades he is on an extradimensional exile from his home world (and rendered temporarily unaging), he just keeps learning and adding things to it.

Film

 * Gymkata is an entire film built around the blending of Western gymnastics and Eastern martial arts to create a new fighting form.
 * Throughout the Star Wars universe, there are seven different forms of Lightsaber fighting.
 * Arguably averted or subverted; what we see on screen is based on practical fighting systems.
 * Gun kata in Equilibrium and Ultraviolet: the art of dodging bullets by estimating statistically where they would land and not have any body parts there.

Literature

 * Dune has the Weirding Way, which is derived from the Bene Gesserit prana-bindu skill.
 * Due to the presence of kinetically-sensitive personal Deflector Shields, knife and sword fighting styles have evolved to include slow strikes that can penetrate said shields.
 * To say nothing of the Honored Matre fighting style that involves incredibly fast kicks delivered with no nervous input from the brain, which makes one wonder what triggered the attack in the first place.
 * In Isaac Asimov's later Foundation prequel novels, Hari Seldon is skilled in "Helicon twisting," which isn't described in detail.
 * Logan's Run (the 1967 book that the 1976 film was based on). Sandmen use the hybrid martial arts style Omnite.
 * In David Weber's Honorverse, the Manticoran military uses Coup de Vitesse.
 * The Judo-derived Neue-Stil Handgemenge is also demonstrated.
 * Robert Heinlein's novel Podkayne of Mars mentions a martial art called "Kill-Quick", which Podkayne's mother is skilled in.
 * Sinanju from The Destroyer
 * The Kingkiller Chronicle books feature the Ketan, a martial art practiced by the Ademre.
 * There is also Naked/Kill from Shibumi by Trevanian.
 * Vasili Golovachov's The Envoy introduces Rossdao, a Russian martial art based on ancient Russian combat styles and is said to be equal to any East Asian martial art. While the details are not described, the protagonist learns how to put out a candle from a distance (similar to a Real Life Wing Chun technique), jump and kick from a kneeling position, evade a submachinegun, etc.
 * Golovachov loves inventing fictional (Russian) martial arts. In his Catharsis series, he introduces a martial art that has its roots deeply in magic, and the fights take place at Super Speed.
 * In Leonid Kudryavtsev's Star Corps Agent, a Bounty Hunter challenges the titular protagonist to a fight using a martial art called Handasiri-ha. Somehow, a master of this (even a regular human) is able to move at Super Speed to the point where a fight that takes up two pages is actually only about 5 seconds in real-time. The basic fighting stance involves arching one's back in a cat-like manner, spreading one's arms, and tilting one's head slightly. The bounty hunter is also a Human Alien and has more joints than a human, allowing him to use more complex moves. A single successful strike can break one's spine or even kill on the spot.
 * Several moves and stances are named but not described, such as Spirit Windmill, Twist, Griffin's Wing, and Deadly Spinner
 * Sherlock Holmes in his home series knows a Japanese wrestling style called "Baritsu". If that's an example of this trope, a misspelling/legal dodge of Bartitsu (a real life style which doesn't match the description since it's from England, based around Cane Fu, and would be anachronistic ), or something else is debated among fans.
 * The Shadows of the Empire novel introduces Teräs Käsi (not quite Finnish for "steel hand"), which is described as extremely potent and rivaling a Jedi's ability even in the hands of a non-force user. As the only non-species specific unarmed combat system with a proper name (instead of just being named for its users) to appear outside of RPG books, it got used extensively in the expanded universe and even appearing in the title of a (not very good) fighting game.

Live-Action TV

 * Star Trek
 * Star Trek: The Next Generation: The Klingon martial art Mok'bara, which includes unarmed combat and the use of traditional Klingon weapons such as the bat'leth.
 * Several Mok'bara katas are mentioned to be very similar to Tai chi chuan.
 * Doctor Who has Venusian Aikido, which was practiced by the Third Doctor. It was hard for two-armed beings to learn because Venusians have six arms.
 * Time Trax: Mosh-ti was a 23rd century occidental improvement on the martial arts.
 * Cole on Tracker had a martial-arts fighting style that relied on both his and the fugitives' ability to move faster-than-human, and sometimes made use of Cole's hyperspeed ability for brief periods.

Tabletop Games

 * In the Dungeons & Dragons setting Forgotten Realms, the elves have a sword-fighting style called Bladesong, it is described as being deceptively graceful and appears like a dance. The focus of the style is on putting the opponent off balance before striking home with lethal force.
 * Shadowrun has carromeleg, an elven martial art similar to capoeira, with whirling, dance-like movements.
 * In Traveller, there are a number of these. Notable are styles made for the ayloi an artificial claw worn by humans fighting Aslan style.
 * Inspired in part as it is by Eastern mythology, Exalted has many of these (mostly powered by Essence).
 * The Palladium RPG Ninjas And Superspies included, among others, Lee Kwan Choo, a non-violent martial art that stunned opponents by almost making lethal strikes; presumably it was less effective in a setting where Everybody Wasn't Kung Fu Fighting.
 * Mage: The Ascension features a hybrid mental/physical martial arts discipline practiced by the Akashic Brotherhood simply called "Do."

Toys

 * Transformers have included several Cybertronian martial arts, like Circuit-Su or Crystalocution. The best-known one is Metallikato, mastered by the Decepticon Bludgeon.

Video Games

 * Echani, used by the Echani people in Star Wars: Knights of the Old Republic II: The Sith Lords.
 * Insult Swordfighting in the Monkey Island series, which is a combination of fencing and insulting the opponent as a form of art.
 * There's also Monkey Kombat in Escape from Monkey Island and a mention of other Insult sports (you actually engage in a round of Insult Armwrestling in the game).

Web Original

 * The Onyx Eye tong in Academy of Superheroes practices their own unique martial art, the Onyx Way. It includes horribly painful torture techniques, incredibly effective blindfighting skills and, for the most skilled practitioners, immunity to telepaths.
 * Grandmaster of Theft features Cassidy's Bellavado style she created. While her foundation style is Crawford Combat Discipline, Cassidy branched off of that to change to build Bellavado which uses graceful movements, cunning, and taunting.
 * Crawford Combat Discipline is based in self-defense, counterattacks, and disabling one's opponent.