Gun Fu is a catch-all term for the fancy moves Hong Kong action movie characters (and Western films inspired by said Hong Kong action movies) perform with their guns. It's essentially martial arts... WITH GUNS!
Essentially, the main point of Gun Fu is the liberal application of Rule of Cool to firearms. Expect lots of Guns Akimbo, Pistol-Whipping, and a heat-packing version of the Offhand Backhand. While pistols are the most common weapon, it can also be done with anything else you could reasonably consider a firearm - Uzis, the Sawn Off Shotgun, even rocket launchers, as long as you hold it in your hands and fire it. Occasionally, they mix in a little standard martial arts.
It's become very common in modern action movies. Why? Rule of Cool, that's why!
John Woo pretty much invented it in 1986 with A Better Tomorrow, which launched the Heroic Bloodshed genre in Hong Kong. Shortly afterwards, these sequences began popping up everywhere. Chow Yun-Fat, who became an iconic image with a gun in each hand, starred in most of Woo's later films.
Now it must be clear that this is notGun Kata. It's a close relative. That trope is more about strategic dodging and aiming with guns, while this is about acrobatics with guns. Both are graceful and cool to an almost obscene degree, but Gun Fu is probably the more plausible of the two. Although both involve Improbable Aiming Skills. And yes, you can use both at the same time.
Has roots in Wuxia. Compare Implausible Fencing Powers, just with swords.
Kenichi: The Mightiest Disciple has a character named Jenny who is a master of using guns as if it were a martial art. She acquired such an ability on account being the daughter of a famous gun collector.
Kenichi's father, of all people, is capable of some of this; he managed to reload a giant shotgun with one hand, something that resident weapons master Shigure said wasn't possible.
Played straight and subverted with Riza Hawkeye from Fullmetal Alchemist, depending on the situation.
Give Mana Tatsumiya a firearm or two and she's a death machine, capable of wiping out a crowd of people all around her without turning around. In one instance, she's able to snipe dozens of people (with rubber bullets, don't worry) from all over her improbably large school campus by ricocheting rifle shots off of various buildings.
Given that Black Lagoon is the lovechild of John Woo and Quentin Tarantino, it should come as no surprise that Revy engages in this pretty frequently. In her fight against Ginji she frequently uses her pistols to block his katana.
And then there's Mr. Chang, who is pretty much as close to Chow Yun Fat's various John Woo film characters as a work of fiction can get without getting sued for copyright infringement. It's implied he's the one who taught Revy the ways of Gun Fu.
Trigun is pretty much made of this: Vash, Wolfwood and the Gung-ho Guns in particular. "Derringer" Meryl has a few moments as well.
Spike's battles with Vicious in Cowboy Bebop seem to fit in under this as well.
Yoko of Tengen Toppa Gurren Lagann does this with her Sniper Rifle using it as a staff to take out the beastmen surrounding her during one episode as well as in the movie.
Although not quite as flashy as most examples since it's Evangelion, the epitome of not really being awesome, Misato's big scene in End of Evangelion involves her gunning down a whole squad of JSSDF guys while running at a dead sprint before bashing the remaining guy into a wall with her gun and then shooting him point blank. Rather impressive when all other gunfights in the film are either the JSSDF casually strolling through the base picking off helpless NERV people, or Makoto and Shigeru ducking behind their work station while JSSDF pins them down with constant fire and occasionally returning fire.
In the beginning flashback sequence of Afro Samurai, Justice duels with Afro's father. Justice's weapons are a pair of six-shooters while Afro's father wields the BFS that Afro wields in the present. Afro's father may be able to deflect Justice's bullets with his sword, but Justice uses his guns to parry Afro's father's attacks and manages to do quite well in close combat with him.
Canaan practically runs on this, the titular character the biggest example.
Hong Kong fight choreographer Corey Yuen (who was one of Jackie Chan, Sammo Hung and Yuen Biao's best friends during their days in the China Drama Academy Peking Opera School) is distinguished in his ability to mix hand-to-hand combat and gunfighting, two styles of fighting that are not often used together successfully in Hong Kong action films.
A sort of nascent example turns up in some Spaghetti Westerns — the lead who is not Lee van Cleef in The Grand Duel flips and rolls through gunfights, once shooting a Mook while falling upside down after propelling himself into the air with the aid of a cart and a falling body.
Kick-Ass has Hit Girl who is improbably good with guns. At one point she more or less flies down a narrow hallway, gunning down mooks, reloading from her belt, gunning down mooks, reloading by flinging the clips into the air and catching them with her gun, then gunning down more mooks before running out of bullets. Did we mention that she's dodging so well she's practically flying? Oh, and although she's willing to nonfatally shoot someone, everyone is finished off with a headshot. And she's 10 years old.
Maggie Cheung's character in Heroic Trio fights with a shotgun and a machine gun in two scenes, wielding them as if they were swords.
The Long Kiss Goodnight: One of the earliest western examples before John Woo migrated to America. Noteworthy examples include:
Leaping out of an exploding building and using an Uzi to shoot up the frozen lake below to soften the impact of landing (having already used a revolver to soften up the window before leaping through it).
Loosening a cable tied to a burning corpse hanging from the top of a bridge's bannister, making the corpse drop; holding onto the rope and allowing the corpse's weight to pull you up right next to the helicopter 50 feet above you and emptying the mag of the Uzi you just grabbed from the falling corpse as you passed it into your evil-ex-lover at point blank range.
Shadowrun created a Martial Arts fighting style based on this Trope called Firefight, and noted that it came from the improbable fighting styles of movies (trideo). From SR4 Arsenal, page 157: "In 2068, Ares Macrotechnology unveiled a completely new martial arts form based on the popular image of a gunfighter whirling through a melee with a pistol in each hand, shooting as much as punching and kicking. The product found its market in eager young gunslingers raised on a steady diet of trideo action flicks." The trope is alive and well, even in 2070.
Notably the martial arts style only grants a reduced penalty to firing guns (from -3 to -1) while in melee range as well as a bonus 1 to Dodge (melee).
In addition, the Gunslinger Adept in SR4 was designed with Gun Fu in mind, using magic to augment his gunfighting skills.
Also, with GM approval you can take a martial arts specialization in clubs, in order to use your two pistols in melee combat.
In a rare attempt from Catalyst Games to add a bit of realism: Your guns will break if you bash them into people to much, of course you could just grab melee hardening as a mod and go to town, there is a unique pleasure in bashing a elf over the head while blowing a hole in the head of an ork
Exalted has the Righteous Devil Style. It's a martial arts style with a list of Charms (magical abilities) that require the martial artist to be wielding flame pieces or firewands (one-use short-range flamethrowers), that are the setting equivalent of pistols or rifles. Of course, a character could alternatively pick up a plasma tongue repeater or two, which are magic revolver flamethrowers.
Don't forget Golden Exhalation Style, for when you want to reload your gun with personal life energy, parry bolts of fire, and reload your weapon with the flame-stream of your enemy's gun.
Cthulhu Tech gets this in the Vade Mecum companion book. Your standard pistol styles are all there, along with Rifle-Fu.
And then there's the Gun Schticks one can get if you create a gun-using character in Feng Shui, most of which are meant to simulate the crazy-ass shit that Gun Fu practitioners can pull off in Heroic Bloodshed movies.
GURPS just straight up named its supplement on cinematic gunfighting "Gun Fu".
Every character in Hong Kong Action Theatre, in addition to knowing Kung Fu, can also shoot with gusto using his or her default Skill rating.
Scion, while not inherently an example of this trope, is a game where the player characters are half-divine heroes with reality-bending powers and, frequently, celestially-augmented weapons (including handguns). This is a setting where Gun Fu can be practical as a preferred combat style.
The Fudge Factor article Fudge Firefight II introduces a bunch of knacks that are built to allow this. Jumping through windows firing a pair of pistols is standard practice.
Since Hot Rods and Guns feature strongly in anime, Big Eyes, Small Mouth has "Gun Bunny" as one of its attributes. As the name implies, the attribute covers over-the-top feats that cinematic gunslingers pull off. The third edition lumps everything from the Gun Bunny and Kensei lists into the "Combat Technique" attribute.
The Hero System martial arts supplement includes "Zen Riflery". (Alternate name: Woojutsu.)
The RiftsSourcebook China 2 has the Gun Master O.C.C. They are warriors trained in Tao Jen Qiang, "The Way of the Patient Gun." It is a martial art that lets them become one with guns in ways that would make Chow Yun Fat look like a novice. For instance, at first level they can kill MDC monsters with SDC bullets, which is normally an impossibility in Rifts (see Chunky Salsa Rule above for more details). At higher levels they can shoot ghosts.
Tomb Raider: You have to appreciate Gun Fu, when you draw an M-16 while flipping backward in the air and successfully target some mook on the balcony below you.
Devil May Cry's Dante is a Gun Fu master, though his various swords are his more prominent weapon.
In Devil May Cry II, it's even possible to hover in midair by firing both pistols downwards.
Devil May Cry III takes it to the next level. On a double jump, you can flip upside down, spin and shoot, flip back up, flip upside down AGAIN, spin and shoot, and flip back up in time to land on your feet.
In Shadow Hearts: From The New World one of the available characters is a towering Native American who uses Gun Fu with six-shooters in Guns Akimbo. His Special Power is actually CALLED 'GUN-FU' - and his basic attacks are actually Kung-Fu katas with gunshots.
Stranglehold is a video game sequel to John Woo's Hard Boiled (interestingly enough there are talks of making a live action movie for the game) and does an excellent job of replicating the Gun Fu of the movie in a videogame.
Big Boss and the Boss of Metal Gear series developed a form of CQC that integrates a knife into a gun-holding stance, where the practitioner will hold a combat knife in the last two fingers of their off-hand, with the thumb and other two fingers still on the gun as normal (this produces some off grips on some rifles where just adding the knife with the off-hand where it normally goes would result in it stabbing the magazine; in Metal Gear Solid 4, we can see Snake using a sort-of claw grip to prevent this problem with his M4 and AK-102.) In cutscenes, this is taken much further, with melee spectacles involving the snatching of full-sized rifles out of someone's hands and having it ready to fire in under a second, throwing to the ground with a rifle since both hands are tied up holding it, and breaking down someone else's gun before they can fire it.
Vincent Valentine of Final Fantasy VII has been established as utilising this in the spin-offs, in the original game he was more of a straight up gunslinger.
Total Overdose, a Robert Rodriguez homage, becomes progressively more Gun Fu oriented as maximum adrenaline increases. The whole acrobat range of stunts are unlocked from the beginning, and the majority of sidequests are intended to introduce and exercise the skills.
The martial arts discipline Krav Maga as taught to Israeli special forces can integrate a rifle or pistol into your attacks. This can make the name of the martial art somewhat of a Non-Indicative Name, as it literally means ‘touch combat’.