Tower of God - It is implied that the weapons of the 13 Month series cause this, since Eurasia Enne Zahard started to go on a random killing spree after receiving the Colourless December. It also applies to Anak's Green April, which seems rather bloodthirsty and activates when Anak gets angry.
Belkar Bitterleaf of The Order of the Stick, 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.
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).
Bangladesh DuPree from Girl Genius, 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.
In fairness, that one wasn't her fault. Skewering Zulenna, one of the students on Castle Wulfenbach, when it was very much not necessary and a potential political problem for the Baron, now, that was all her.
Kamekaze Kate is a car racing Ax Crazy in Misfile.
At first at least 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
Electric Retard is full of them. One even happens to be a naked guy with an axe.
Axel of the Ansem Retort 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.
Cousin Dougal from Platinum Grit, a psychopathic immortal Scotsman who lives to stab.
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.
Il'haress Kharla'ggen Vloz'rezz from Drowtales 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.
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.
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.
In fairness, the latter action was committed to save herself and her friends from being erased from existence by the Scratch, so it's a bit ambiguous as to whether it qualifies.
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.