For various reasons, Doesn't Like Guns is a common thing with comic book style superheroes and supervillains (whether it's ethics, style, or something else). While Proto Superhero vigilantes like The Shadow or The Lone Ranger often went armed, the Golden Age supers who came after them typically relied upon their extraordinary abilities over firearms. Even before The Comics Code was written, it was rare to see superpowered heroes with guns. Then some heroes who broke this rule caught on, and soon more and more heroes and villains began using guns. This soon became closely associated with the Nineties Anti-Hero, and therefore also fell out of favor when that trope did.
This doesn't have to be just projectile firearms. Lasers will do as long as they are used more like firearms than Ray Guns. Heck, even flamethrowers and bazookas can count. Bonus points if the character is also wearing a Badass Bandolier.
Note: To count, a character has to meet two requirements:
The character has to be a comic book-style superhero or supervillain.
The guns have to be one of the prominent "powers" of the character, not one of the character's lesser-used weapons.
Death The Kid from Soul Eaterhas Liz and Patty, who transform into guns.
The earliest comics featuring Batman had him using guns. This got retconned moderately quickly once writers realized that having Batman kill all of his adversaries in one issue meant that he'd have no one to fight later and they'd have to rack their brains thinking up new ones too often. Once he started hanging around with Robin and it was revealed his parents had been killed by a gunman, it went away entirely. In modern continuities, this gets a Call Back every so often, usually under the guise of a "Year One" story or a alternate universe. The main timeline Batman has used a gun against another sentient being with aggressive intent only once: in Final Crisis, after Darkseid has become such a threat that everything is on the table.
It's rumored that the actual reason Batman stopped packing heat is because Batman was originally based heavily off of The Shadow, and giving him a gun as well a rich playboy secret identity (something The Shadow did first) would make the two characters so similar that a lawsuit might be tossed their way.
Arsenal from Teen Titans used a pair of handguns and other weapons. He stopped using guns for a little while (but kept using things like crossbows) but returned to using them in The Outsiders. Then he became Red Arrow, and ditched every weapon he had other than his trusty bow and arrow.
When Superman found himself in a depowered state after his resurrection, he proceeded to arm himself with an armory of alien energy rifles.
Cable of X-Force. His guns have a tremendous variety of size and improbability of design. For example, one barrel the size of his head, and several smaller barrels beneath? (This from Phalanx Covenant.) He routinely uses guns larger than his own body, and Cable is a large man. Though he has immense telekinetic powers, Cable long relied on guns because the bulk of his power is spent simply keeping an incurable virus from killing him.
Bishop of the X-Men, as a cop from future not unlike that of Judge Dredd, used guns when he first arrived, and an ongoing Character Development plotline for him was learning to tone it down and not use lethal force. He also had the power to shoot energy rays, but used guns frequently as his power depended on external sources of energy to redirect. One version of his guns actually channeled his own powers.
Also from DC Comics is Wild Dog, who looks like he should be a parody of the trope, but sadly isn't.
Max Allan Collins noted in Amazing Heroes #119 that he created Wild Dog as a sort of modern update of Zorro, The Green Hornet, and The Shadow, who all predated Superman and Zatara, and Collins carefully distinguished between a costumed hero and a metahuman hero. Collins did not intend Wild Dog as "super".
Ballistic, one of the "New Bloods" from DC's Bloodlines event. Another one, Gunfire, had the power to turn any handheld object into a gun.
Several of the characters in Watchmen, notably The Comedian.
The Tick: Guns and superheroes don't mix. Seek professional help.
He does get professional help, though he still has to apply extreme-ness to one word...
''As you know, I used to be a very violent person. I'd resolve all of my problems with Gh-gh-g-g-GUNZ!!
Hitman. His powers are telepathy, X-ray vision, and lots of guns — not necessarily in that order.
Captain America's original incarnation had him using guns in addition to his famous shield, since he was a Super Soldier fighting the Nazis during World War II. His movie also aims in this direction (Justified, since it's During the War). As you can well imagine, fan reactions are... somewhat mixed. In The Avengers movie, he mostly sticks with his shield, though he still picks up guns a couple times.
Bucky also used a gun when he took up the identity of Cap.
Steve has started packing heat again as Commander Steve Rogers, Head of S.H.I.E.L.D.
In-universe, Rogers explains that he used a gun when he was fighting a war, but what he does now is law enforcement and he considers himself capable of stopping crooks without resorting to killing them.
During a period where he lost/repressed his primary powers (eye-beams), Cyclops of the X-Men carried a pair of pistols for offensive purposes in the field. It complimented his secondary power of innately understanding angles and trajectories, letting him pull off incredibly accurate and tricky shots.
The Crimson Avenger in The DCU. Both the original in his Coat, Hat, Mask phase and the Nineties Anti-Hero successor. The legacy character takes this further, claiming that the original CA's chest emblem during his superhero days wasn't a sun - it was a bullet hole.
Grifter of the WildCATS and Wildstorm Universe, although sometimes possessing psychic powers, usually favoured Guns Akimbo, switching between his VADs and a variety of mundane pistols.
His brother Condition Red, AKA "Grifter, Jr." doesn't have any powers, but his firearms expertise was enough to get him recruited to Savant and Majestic's WildC.A.T.s team.
Moon Knight has on ocasion used weapons. But then again, he is a former mercenary and soldier (And in the Ultimate Universe, a former Navy Seal), and is known to be a dark subversion of Thou Shall Not Kill, so its not exactly out of place. Its also one of the characteristics that seperate him from that otherKnight. His general aversion of this trope has less to do with morality than with pride, i.e. not wanting his opponents to think they intimidate him.
This carries over into the movies: during the final fight when they're being attacked by drones in Power Armour, Iron Man punches them or uses his repulsors while War Machine just unloads with the cannons.
In one episode of Don Martin's parody Captain Klutz, the eponymous hero is confronted by an evil old-lady villain who attempts to escape using the fact that Klutz's superhero code prevents him from hitting her. Klutz shoots her instead.
The current incarnation of Venom, Flash Thompson being former miltary, uses various firearms, along with the powers provided by the alien Venom symbiote suit.
Before him Jack T Chance used a gun. Because GL rings couldn't kill back then, he carried a weapon to finish off his opponents after beating them with the ring.
It should be noted that both Baz and Chance use their guns as backup/secondary weapons, rather than as main components of their power set (Chance because his planet is full of murdering psychopaths, and Baz because his ring was on the fritz and he's got it as a matter of practicality in case his ring gives out on him). Didn't stop a lot of people from getting worked up thinking this trope was in full effect with Baz, when they first saw that the first middle-eastern Green Lantern used a gun for no (apparent) reason, before it got explained in-comic.
In Black Summer, the group of cybernetically-enhanced supers call their gifts "gun enhancements" and they do indeed wield powerful, dangerously high-tech pistols in addition to their suite of powers.
In Spawn, Al Simmons was a highly skilled commando in life. He still makes uses of his skills with firearms as Spawn since using them is familiar to him and it helps him conserve his Hellspawn powers.
Exaggerated in the film adaption of Kick-Ass, where Big Daddy and Hit Girl's arsenal includes a staggering number of pistols, submachine guns, assault rifles, sniper rifles, hunting rifles, shotguns, two M134 miniguns, and a bazooka.
The Spider. Similar to the Shadow, the Spider frequently dealt justice with a pair of blazing automatics.
In Relativity, Ravenswood is a private eye packing heat, and when he graduates up to being a superhero, he keeps the gun.
Harry Dresden of The Dresden Files is a wizard P.I. who's essentially written as a comic book superhero, and it often catches both monsters and other magic-users off guard to discover he also carries a gun.
SPD and Time Force take it furthest, as they do have a police theme and police officers have a noticeable lack of magic crossbows and axes. The Time Force weapons are the Chrono Blaster sidearms, the V-weapon BFGs, and the Vortex Blaster, which is the giant Wave Motion Gun you get when you combine the V-weapons. In SPD, we have small guns when unmorphed, bigger (but not V-weapon level) guns when morphed, and the Finishing Move is the giant cannon the Robot Buddy transforms into. SWAT mode's weapons are these big automatic-rifle-things. Nothing like standard Ranger weaponry is anywhere to be found, and most upgrades amount to "needs more gun!" Even the robots carry guns (though the main one also has the more-expected sword) and one turns into a BFG that can operate in orbit (or be wielded by all of the other robots.)
In season one of Who Wants to Be a Superhero?, the Iron Enforcer's gimmick was a incredibly huge cannon mounted on his arm. Subverted in that Stan the man was never really all that excited over superheroes with guns, let alone huge ones like that, and between his gruff attitude and less than stellar challenge performances he ended up getting the boot. Then on the way out (portrayed as him literally walking out a back alley, when a nearby TV suddenly comes to life) Stan said that he finally figured it out: Iron Enforcer made a lousy hero, but DARK Enforcer made a greatvillain!
Just about every Heisei Era Kamen Rider series features at least one hero/form that uses a gun as it's main weapon.
Most fitting is G3 from Agito. A Rider made by the military, there's no Rider Punch, Rider Kick, or supercharged medieval weaponry to be found. Instead, his main weapon is a gatling gun. In a pinch he has pistols, and if the gatling gun fails, it's time for the rocket launcher!
The Scarlet Spectre of Freedom City's Time of Vengeance campaign, is a B-Level vigilante who, lacking superpowers or much money, fought crime with her father's .45 pistol.
The Harbinger of Justice in Dark Champions is this trope taken to almost parody level, but the setting contains plenty of straight examples as well.
Somewhat encouraged by the rules — in the Hero System, buying powers through a Focus, especially an Obvious Accessible one like most guns would normally be, can grant a significant character point cost break (up to 50% for an OAF) at the cost of losing access to the power if disarmed or otherwise deprived of the focus item. Which for players who don't mind living with that occasional handicap leaves that many more points over to improve their character's competence in other areas.
City of Heroes has the Dual Pistols and Assault Rifle powersets for ranged archetypes (blaster, corruptor, defender). Also, Thugs masterminds lead a group of gun-wielding henchmen and have their own pistol attacks.
The Masterminds also have the Mercenary powerset, which works like Thugs, but with assault rifles.
Robotics Masterminds get a Pulse Rifle which straddles the line between this trope and Frickin' Laser Beams
And now they have just introduced the Beam Rifle powerset.
Champions Online contains the Munitions powerset. This includes everything from dual pistols as the lowest level attack (and several higher level ones), through submachineguns, shotguns, assault rifles, a minigun, a rocket launcher, and more.
Eldritch of the Whateley Universe. The fact that she is Nigh Invulnerable and has magical abilities doesn't stop her from packing heat. In the Team Tactics course at Superhero School Whateley Academy, she shows up carrying an M16 with an M203 grenade launcher slung underneath. The course is taught by a Gunnery Sergeant and a retired admiral with Spec Ops experience: neither of them are surprised.
In fact, Bladedancer asks Eldritch for gun training. No one expects the Chinese martial arts nut with the magic sword to also be packing an automatic.
Many many more examples, even in the school itself. The Grunts are Whateley's JROTC group, students with weaker powers pack heat, and devisors/gadgeteers design their own guns. Tinkertrain and Flashbang build guns that look like they were designed by Rob Liefeld.
From Worm, Miss Militia's power is explicitly the ability to create any weapon she wants, fully loaded, unable to jam, with whatever ammunition and attachments she wants. She almost always uses this to create guns of various types. One added advantage of her power is that she can use nonlethal ammunition without any drawbacks; if the gun does jam, she just reforms the weapon instantly.