Black Mage. He's kinda the anti-White Mage. He views everyone around him as a target, defaults to murder as a means of social interaction and has been known to hurl himself long distances by setting off a Fantastic Nuke inches from his own face - not as a means of transport, just because he's that eager to kill. At one point we learn that he prefers to urinate on dying people (although an anthill will do, in a pinch) because it just feels like he's wasting his time if someone isn't being hurt.
Berserker is usually a perfectly sane, polite, downright classy fellow. Then he goes berserk.
Kary, the Fiend of Fire, is so willing to follow whatever sadistic whim pops into her head that she ends up wiping out most of her own minions before the Light Warriors even get there.
Galen from The Adventures of Wiglaf and Mordred. Her favorite "patients" seem to be her fellow teammates (or her daughters teammates, much to her daughters annoyance).
Axel seems to go out of his way to inflict grievous bodily harm on his "friends", and generally murders anyone who happens to exist anywhere within a hundred mile radius of himself.
Namine: You couldn't go 10 seconds of diplomatic immunity before murdering someone?! Axel: I wasn't even listening to you. I just wanted to murder a dude.
Larxene is, arguably, even crazier having destroyed Disney Land and everyone/thing inside it just because she wanted funnel cake.
Axe Cop is pretty violent and armed with an Axe most of the time, but this is usually just bad news if you are a bad guy. However in this strip he goes pretty Ax Crazy after the wrong candles are put on his cake and kills indiscriminately.
A Broken Winter introduces us very early on to Kuroda's wife, who killed their son (according to Word of God) as a protest against killing children. In their words, "Logic at its finest". She also killed the family dog and tried to kill her husband too.
If I'm not perfect now, I can always be the most perfect thing left alive.
The Continentals: The escaped mental patient known as The Mangler, the sinister and psychotic Mr. Qwist (hired man of the equally bent Dr. Daniel Abbeline).
Il'haress Kharla'ggen Vloz'rezz is the personification off Ax Crazy. And considering that the Woman Behind The Woman that was the only thing capable of keeping her in check and from going on an unstoppable killing spree was beheaded in a recent chapter, she will most likely become further Ax Crazy still as the story progresses. Or, considering that it was this woman who originally drove her Ax Crazy, it's within the realm of possibility that she might calm down to just plain crazy.
In El Goonish Shive, Damien killed everyone in the lab Grace was born in, wanted to massacre Earth's population, and was getting ready to kill Grace's friends before she lost her temper.
Ennui GO!: Asher, Izzy's first artist. Hates women and people in general and tries to kill Izzy. Twice.
Lothar Hex from Exterminatus Now is psychopathic enough that he regularly attempts to cause harm to next door's dog for no reason, but in order to REALLY get him riled up, all you have to do is ruin his hat. At which point, don't expect too many of your limbs to still be attached.
Bangladesh DuPree. Rather indicative is that she regularly counts how many ways she can spell "eviscerate." Although Baron Wulfenbach and his son Gilgamesh have some control over her... usually.
Klaus: DuPree. When I say the words Alive and Unharmed — do any neurons actually fire in that brain of yours? Bang: Um—No Sir! Klaus: I thought not.
Really, Othar and any of the Jägers fit this trope to the letter. The Jägers at least have an excuse, though, being bioengineered supersoldiers selected for loyalty and ferocity, not brains.
Truly taking the cake, though, is Castle Heterodyne's AI. Its selective memory turns the most innocuous commands into a massacre. Really doesn't help that it was built and programmed by Ax-CrazyEvil OverlordMad Scientist types, and it's gone even more nuts due to being broken, so it's almost impossible to tell which particular bits of Ax-Crazy are bugs and which are features. This is how it remembers its first conversation with Agatha:
Castle: How may I serve you? Agatha: Oh goody! Who can you kill for me?note She asked about its defensive weapons. Castle: I can kill things in the sky. Agatha: Yay! Do that! Kill everything in the sky!note She ordered the airspace cleared of intruders.
Doh Gyeom while under the influence of his alter-ego from Gosu happily slaughters through droves of people to satiate his bloodlust. The same issue also occurred for Gyeom's late older brother, Doh Gyeol.
Also, Eridan goes off the deep end too, murdering two of his friends in cold blood and single-handedly destroying any hope of his species long-term survival.
Caliborn. He is entertained by death and wants to kill everyone, especially his sister Calliope.
Jack Noir. At one point, he's stuck in jail with nothing but a pumpkin full of knives. He then proceeds to murder everyone around him, even when he's trying to keep at least one of them alive to open his cell.
Meenah, also. To the point where she greets people by trying to kill them, and blew up herself and all her friends, as well.
The Order of the Belligerent Knights are an organization of insane psychopaths and berserkers with such creeds as "Let's cut God to see if he bleeds!" and "If it has a pulse, take its skull!" Unfortunately, they are also some of the most powerful individuals in Creation, and that's really saying something.
Jagganoth is one of the seven Demiurges who rule all of Creation. He was originally an angry and powerful man who conquered one-seventh of the multiverse with nothing but his own might, but then he left to try and find a purpose. He found one and returned as a literally invincible juggernaut immune to any and all harm. He is as strong as the other six Demiurges put together, and the only thing keeping universal war from reigniting is their fear of him. And just for extra fun, when the Belligerent Knights encountered him, they tried to kill him and failed. They promptly decided that the only logical conclusion was to worship him. So now the most dangerous thing in all Creation has the service of the most dangerous Knights in all Creation.
Rocky and Freckle in Lackadaisy are heroi— um, protagonist examples. While Rocky is friendly and upbeat and at worst a Jerk with a Heart of Gold, and Freckle is something of a Shrinking Violet, put either of them in a stressful situation and mayhem ensues as Rocky turns into an unhinged Pyromaniac and Freckle becomes a gun-toting berserker. Rocky, in particular, has been getting worse following a severe head injury.
Kamekaze Kate is a car racing Ax Crazy in Misfile. At first, anyway- after she was freed from her sister's influence she got a lot better. And her race with Ash ended in a traditional Defeat Means Friendship moment, that is Ash's defeat by Kate.
My Deepest Secret: Elios is a very downplayed example. While he never goes out of control or visibly insane, it does tell you something when his first reaction to a cat peeing on his girlfriend’s shoe is to kill it. Also shown when he attacks Brian. Judging by his level of preparedness, he was already planning to attack him before he tried to rape Emma, which means the attack was likely not just because of that but out of jealousy.
Belkar Bitterleaf, described as "a Chaotic Evil halfling who is constantly trying to murder anyone who gets in his way! Or looks like they may possibly be thinking about getting anywhere sort of near his way at some unspecified future point, just to be sure."
"I AM A SEXY SHOELESS GOD OF WAR!!!" "Yes, run, my little chunks of XP!"
The Big Bad, Xykon, who will (and has) kill anyone, for any reason, usually on a whim.
Jekkel from Silver Bullet Nights. Despite his slender, almost androgynous looks, Jekkel is a force of nature when he snaps or even when he's just set on someone by his girlfriend. He doesn't care about his own safety - all he cares about is killing the opponent at all costs. Of course, it helps that Jekkel is a nearly-immortal vampire with a Healing Factor.
Even by demons' standards, Azurai is a violent, temperamental sadist who's just itching for a reason, any reason, to bathe his claws in someone's blood.
Lazui becomes this after her first battle against Kieri, if she wasn't already before. On her way to St. Curtis, she murders an innocent person for his water and laughs. And she only gets worse from there.
Moonshade is a Psycho Knife Nut extraordinaire who goes Laughing Mad when St. Curtis burns, has murdered at least two Guardians thus far, and murdered his daughter, Rhea, so no one else of Moku's lineage will challenge him. He ponders killing her again with the seriousness of deciding what to eat for breakfast in the morning. Some of the worst demons are more rational and empathetic than him.
Oasis moves in and out of this in Sluggy Freelance. Her mental state is in tatters, and each apparent resurrection shifts it. Even in her more lucid moments, though, she realizes how close she is to violent mayhem. And heaven help anyone nearby if she activates Override B-1.
Norman Gates is a violent, sociopathic Bomb Throwing Anarchist who can barely go ten minutes without committing assault and/or vandalism. His future self from a timeline in which he turned into an anarchist Dark Messiah figure who led the conquest of a significant portion of the world takes these tendencies up a notch. Present-day Norman beats up chavs and sets fire to trash cans. Future Norman beats up entire countries and sets fire to continents.
Norman's best friend and landlord Richard used to be even worse than Norman when they were both kids, making frequent use of a straight razor... and not for shaving. Unlike Norman, he actually grew out of it (although the police still consider him the scarier of the two).
Mr. Kite: Whatever. Nothing else left to burn, I'm bored, let's get out of here.
Tower of God: It is implied that the weapons of the 13 Month Series cause this, since Eurasia Anne Jahad started to go on a random killing spree after receiving the Colorless December. It also applies to Anaak's Green April, which seems rather bloodthirsty. This is later confirmed to be the work of the Ghost of the 13 Months, a female entity that made a deal with Jahad to drive the Princesses to hate each other via Grand Theft Me.
Nina from Venus Envy — starts out as a Sociopathic Hero of sorts who constantly threatens / injures people and is played mostly for laughs. Then she stabs the main character.
Wolf Keum from Weak Hero. He acts entirely on instinct, fights whenever he feels like it, and doesn't stop until his opponent is a bloody mess. Sometimes he doesn't even enjoy fighting, he just does it out of compulsion. His unpredictable violence has lead to him being known as the most psychopathic of the Union.
In Yokoka's Quest, Hurricane is shown to be this after Yokoka challenges her to a fight, which promptly becomes a Curb-Stomp Battle.
from The Adventures of Wiglaf and Mordred. Her favorite "patients" seem to be her fellow teammates (or her daughters teammates, much to her daughters annoyance).