Byakuya does this throughout the Soul Society arc, since his main power is to break his sword into a cloud of tiny fragments that he can control remotely and he's good enough at Flash Step that he can teleport while appearing to stand still. In his fight with Ichigo he's pushed hard enough that he has to start using gestures to direct them faster, and generally has a Not So Stoic moment.
Zommari Rureaux, in his Resurreccion form, can stay in one spot and simply use his People Puppets and Mind Manipulation powers to make other objects, people, or even your own body attack you for him.
Szyael Aporro Granz has a number of abilities that require no physical effort on his part. He has a liquid that can clone others, wings that can create a voodoo doll, and a parasitic resurrection ability that causes him to regenerate inside someone else's body while rotting them from the inside out.
Barragan Luisenbarn is a Walking Wasteland that causes anything near him to age. Even outside of his Super Mode, it's impossible to attack him without this occurring. In Resurreccion, however, he creates a Battle Aura that surrounds him and can be fired off as a destructive cloud. Being even lightly grazed by it will cause it to spread over your entire body within seconds. The most effort we see him go through is occasionally swinging or throwing his axe—which, by the way, has the same powers he does.
Coyote Starrk can do this, but he chooses not to, because it carries significant risk. Most of his powers do not follow this trope, but his ultimate attack, "The Wolf Pack", summons wolf-shaped wraiths that explode on impact. The rub is that, Starrk is actually two people, and his wolves are controlled by his "other half", Lilynette Gingerback...and therein lies the risk. Each wolf that explodes (or is destroyed by other means) has the potential of permanently killing Lilynette. Which, in the anime, is exactly what happens.
Yukio Hans Vorarlberna, when facing against Toshiro Hitsugaya inside his video game world generally fights like this whilst creating monsters and other creations to fight for him.
As Nodt's primary fighting style works in a similar manner to Byakuya's Zanpakuto; floating spikes that he controls remotely. Later in Vollstandig he has an ability that creates walls of eyes that once they make eye contact with his opponent instills deep fear in them.
Gremmy Thoumeaux prefers to not lift a finger while his Imagination-Based Superpower does the work, in a similar vein to Yukio. Kenpachi manages an attack that forces him to use his hand to block it. Which, as it turns out, still doesn't subvert the trope; Gremmy is a literal Brain in a Jar, so even his "physical" body still turned out to be his powers doing the work for him.
Pride from Fullmetal Alchemist gets thrown around like a ragdoll during certain battles, but he attacks by launching shadowy tendrils from just about anywhere on his body or in his vicinity.
Anyone using a Philosopher's Stone, which prevents the need to use circles, or even movement, to perform alchemy, tends to fight like this. The most prominent user of this tactic is Father, who generally doesn't move a muscle, instead using alchemy to disassemble attacks and erect barriers. Towards the end of the final battle, the moment where he finally moves to stop one of Edward's attacks, instead of deconstructing it with his barrier, is the sign that his supply of souls has finally begun to run dry, leaving him very vulnerable.
In the 2003 anime version, this is essentially the way Sloth fights. She just kind of stands there waving watery tentacle arms around.
Gaara (picture above) is protected by his sand, so for most of his fights early on in the series, he stands by while the sand deflects projectiles and destroys his enemies for him. He does sometimes use his hands to control the sand when finishing off opponents though.
Naruto's chakra shroud has a mind of its own, and can launch its own attacks separate from his own.
Members of the Aburame clan seem to prefer to stand still with their hands in their pockets while their insects fight for them, although this isn't always practical.
Nico Robin specializes in this, though (mostly since Time Skip) she has no problem to go up close and personal when needed. Her powers, from the Hana-Hana no Mi, lets her sprout copies of any of her body parts anywhere, from herself, the ground, walls of building, to people's bodies. She uses them mainly to strangle people or break their necks from afar.
Trafalgar Law, with his Op-Op Fruit, can manipulate position of things within a radius, or "room", as if everyone around him are patients Strapped to an Operating Table. He rarely moves much from his position (aside from using hand gestures) while doing so. Downplayed, though, in that he's also a competent close-range fighter when the situation calls for it.
The Haki of the "Supreme King" can be used this way, arguably. However, given that those on the receiving end instantly faint, it more skips the battle entirely. Rayleigh, Shanks, Luffy and Chinjao have all done this, and once again all of them are incredibly competent fighting normally.
Discussed once - it's mentioned by Pekoms of Big Mom Pirates that LogiaFruit powers who practice this trope fully have short lifespans in the New World, because many fighters there employs Haki which, among other things, can bypass Logia's immunity to direct attacks.
Bartolomeo fights in this way due to him being a Barrier Warrior and a bit of a troll. However, he does move around a lot and stays alert if he's up against opponents comparable to him or stronger.
When Luffy first meets Gecko Moria, Moria just sits against the wall and lets his Living Shadow fight Luffy. Luffy finally manages to get past the shadow by slinging himself over the railing and kicking through the floor where Moria is sitting.
Ryuuho from s-CRY-ed hangs back and allows his Altar, Zetsuei, to do most of the fighting for him. Ryuuho is one of the most powerful Altars in HOLY, and Zetsuei is more than capable of defending Ryuuho from attack while dominating other Altars simultaneously.
Accelerator can unconsciously maintain a reflective barrier, causing enemies to defeat themselves even when Accelerator is wholly unaware that he is being attacked.
Fiamma of the Right's Holy Right ability manifests as a bird talon-like third arm that emerges from his shoulder. It can emerge to defend him from attacks he's unaware of, like Kill Sat strikes, then destroy the attacker.
A minor staple in any Gundam series: If a mobile suit has Attack Drones, expect them to do this once in a while.
JoJo's Bizarre Adventure While the first two parts of the series focus mostly on direct physical fighting, the series evolves into this when Stands (psychic powers given anthropomorphic appearances) are introduced. In most battles, combatants don't lay an actual finger on their opponents, allowing their Stands (And the crazy abilities they have) to do the fighting. Aside from most Stands just beating the crap out of the foe or hitting them with long-range attacks, some Stands are based on remote-controlled use, and some even work without the user being aware of it.
Elfen Lied: Higher-end Diclonius like Lucy and Mariko let their invisible, razor-sharp vectors shred everything and everyone around them while they stand (or sit) in place with a blank, detached look on their faces.
Jig, the protagonist of Stealth Symphony, has a device fused to his back that can detect hostility directed at him, defends Jig from any harm that comes from this hostility, and redirect it back in the same direction. Jig is otherwise an ordinary human teenager with no combat skills whatsoever, but as this device is a Morph Weapon with seemingly no upper limit to what it can take and functions totally independently of Jig's actions, the device effectively renders Jig invulnerable. It is discovered pretty early on that it does not protect Jig from harm with no malicious intent, however, such as accidents.
AKIRA: Tetsuo first evidences true power when breaking out of his cell at the unnamed facility, after being terrorized by the three other test subjects in the dead of night (the monster-sized stuffed toys and pool of milk scene.) The scene of how he deals with the guards as seen in a distant shot in the hallway is particularly horrifying in the small quietness of it, squashing them to pulp against the walls and ceiling while crushing the walls, floor and ceiling around him into spherical depressions, seemingly while in a half-dazed rage and not even looking while he does it. His hike through the city and the ease with which he fends off attack and destroys nearly everything that gets in his way, gives the impression that it is not the boy Tetsuo who is doing all this but some great invisible power that surrounds him, that may be some thing of its own.
X-Men: Magneto almost never does anything physical (aside from frequently moving his hands to direct his powers, which isn't strictly necessary but gives the readers a better idea of what he's doing with his powers), preferring to just stand or hover in place with an amused expression while destroying those around him with random bits of metal.
In The Name OF The King: A Dungeon Siege Movie has a duel between the good and evil wizards. Both of them stand with their arms behind their backs while flying swords fly into one another repeatedly. It's much less interesting to watch than you might think.
Used to terrifying effect in the movie version of Firestarter. In the climax cute little girl Charlie systematically incinerates the evil government agents and scientists that had been experimenting on her after her father is is killed. In playing the scene Drew Barrymore mostly just stands, hands at her sides, as she uses her pyrokinesis to melt bullets in mid-air as she is shot at, causes flames to burn across the ground at fleeing people and sends fireballs hurtling into the Shop's building.
Night Huntress: Mencheres, with his staggeringly powerful telekinetic ability, and Marie Laveau, with her power to summon deadly Remnants.
Having the Fire Shield allows Sonic to enter his "waiting" animation, while also withstanding any form of lava or fire, contact which would normally result in instant death. You can even, hilariously, stand on lava.
A more direct example involving the Fire Shield comes from the very first boss fight, against Fire Breath. Having the Fire Shield equipped, standing underneath where the boss will come down and continually charging a Spin Dash will result in the boss essentially destroying itself.
As Super Sonic, Badniks automatically pop when they make contact.
Super Tails has four Super Flickies circling his head, which will automatically attack enemies and bosses. Boss fights with Super Tails can essentially be won by just standing there and letting the Flickies do all the work.
The Star Cloak in Terraria causes stars to fall out of the sky and injure anything that harms you. If used against weak enough enemies, the Cloak can easily take them out with no involvement from the player.
Mass Effect: in the later stages of the second and third games, on lower difficulties, it's quite possible for Adept, Engineer or Sentinel Shepard to wipe out entire rooms' worth of enemies by hiding behind something and hurling Overload, Warp, Shockwave and/or Incinerate at them, without actually needing to fire a shot or lob a grenade.
In fact, the development team specifically said this is Engineer Shepard's forte, demonstrated with the ability to summon combat drones, and hack hostile AIs to force them to fight on his/her side. When either of these powers are fully maxxed, Shepard can sit behind cover while his enemies get obliterated.
Geth Juggernauts and Primes also have access to combat drones and turrets. Cerberus Combat Engineers can lay down sentry turrets, and the Collectors have Seeker Swarms and Seeker Plagues which hunt down the enemy and shut down their powers while dealing moderate damage.
In Metroid Vania-style Castlevania games, the player almost always eventually receives some sort of ability that gives them Touch of Death. For example, the Wolf/Bat transformations in Symphony or the Black Panther in Chronicles of Sorrow. With these equipped at high levels, the player can just run through most enemies and kill them on contact.
Syndra in League of Legends can cast spells while moving (hovering) and attacking. You can fling all sorts of spells (and their own minions) at your opponent's face without allowing the fight to distract you from merrily farming minions.
Dormammu doesn't really "attack" so much as he casts a variety of spells. Some of them border on Full-Contact Magic due to the way he slashes or moves his hands, but for the most part, he merely gestures or points to make things happen. This is especially the case for his Stalking Flare super—once it's been summoned, it follows the opponent wherever they go and Dormammu doesn't have to do a thing.
Phoenix Wright is a weird example, as he doesn't "attack" at all. Phoenix's damage-dealing moves are all normal actions, clumsy slip-ups, or normal everyday objects that he tosses away. His partner, Maya, even comes out to help by using her Psychic Powers to protect or fight off the opponent. Phoenix himself, however, doesn't really do anything.
As stated in the comics entry above, MODOK doesn't do anything except sit in his chair and press buttons or use psychic abilities.
Reflecting the Naruto example above, Gaara in Naruto Shippuden: Ultimate Ninja Storm 2 and onwards battles in this way too: His attack strings show him just standing in one place, arms crossed, watching as his sand whacks his opponents further and further away. Sometimes, he will lift an arm for one of the stronger moves in the combo. Sometimes, he won't.
The Elder Scrolls: A Conjuration user can do this by summoning high-level servants and familiars to fight the enemy while safely staying in one spot.
You can also summon various creatures to fight for you in Fate. The periods during which they can stay are limited and the opposition can often zilch them, so you may have to keep re-casting the spell. When you get to a certain level on your Charm magic abilities, you can put a spell on members of the opposition to join your side. Cue huge melee fight while you just sit there and watch them beat the crap out of each other.
War Frame: If the Warframe called Ember ever goes up against Infected, all it has to do is activate one of its many fire powers. The Infection use nothing but melee and turn into a crisp before they can get close enough to do anything.
The final boss of Skullgirls never attacks the player with her own hands, instead floating above the battlefield and sending forth her undead minions with gestures and commands.
Kingdom Hearts 2: Sora's Final Form. While he can jump and glide all over the place (Final Form is actually the most mobile form) he never touches the Keyblades as they float around butchering everything within his now vastly inflated striking range. In fact, Final Form almost does a meta version of this trope, as the Keyblades automatically initiate attacks while doing things like using an item, healing, or doing anything other than standing perfectly still. Meaning you can kill hoards of enemies without ever touching the attack button.
Lampshaded by Elliot in El Goonish Shive during the fight between Grace and Damien. He realizes that because the latter has nearly godlike powers (which would end the fight immediately in any other instance), he never actually needed to learn how to fight properly.