Supergirl enemy Reactron is a violent, sociopathic psychopath who gets off on hurting and killing others. He blew the whole Kryptonian race up because Supergirl defeated him in the past and attempted to murder his ex-girlfriend because she had the gall to break up with him.
Though his insanely over-macho dialogue tends to mask it, Lobo is this trope in spades. He murdered the entire population of his homeworld. Hell rejected him for being too much of a troublemaker to deal with. Valhalla, where the courageous dead fight all day, pull themselves back together at sunset, then feast and drink before they get some sleep so they can repeat the process the next day, kicked him out for being too violent. Think about that one.
The Punisher MAX: Oh, so many. Fun game: Take a drink everytime you see a villain who is frighteningly sadistic, violent, twisted, and willing to kill many people without a single trace of guilt. To say that they are violent sociopaths could be a hugeUnderstatement.
Ares so much. He was one of the first members considered for Norman Osborn's Dark Avengers team. Though I suppose it should be expected considering the guy is the God of War. While Ares has shown affinity for all weapons, from spears to bazookas, his weapon of choice is his enormous ax.
Speaking of the Dark Avengers, most of the team is nuts. Bullseye is wildly murderous. Venom can barely keep himself from eating everyone he meets. Even Osborn is constantly trying to hold back the crazy goblin voices in his head.
The second team aren't much better: Ragnarok, Thor's unhinged cyborg clone, June Covington, serial-killing geneticist, Ai Apaec, chimera god prone to torture and bloodletting... Even Skaar, the team's Token Good Teammate - and it should worry you when a Hulk is the Token Good Teammate - has had an Ax Crazy bout.
Bullseye. His homicidal nature gets taken up to eleven in Daredevil #169, where he has a brain tumor that makes him hallucinate. He sees everyone as Daredevil, and goes about murdering random people on the street.◊
The Owl isn't much better. He was nothing more than a crooked financial adviser with explosive anger issues and the ability to glide at first, but after multiple humiliating defeats, he underwent various experimental treatments to grant himself superhuman physical characteristics. They sure did work, but they also did a number on his sanity, turning his bad temper into unreasoning homicidal fury and giving him increasingly strong bestial impulses and urges. It's so bad that even the Kingpin treads very, very carefully when dealing with him.
Matt Murdock's Arch-Enemy Wilson Fisk aka The Kingpin. He started out as a brutal street thug who enjoyed getting blood on his hands. Even as the Kingpin, Fisk still really enjoys physically dominating people and brutally killing them with his bare hands.
Jack O'Lantern definitely qualifies as this. As a kid he had all the textbook signs of being a serial killer/sociopath, like torturing animals for fun. After he was taken in and trained by the Crime Master he used his skills to track down and murder his own parents. He later hunted down and murdered the two guys who previously held the title of "Jack O'Lantern" just to "clean up the brand". He also has a creepy obsession with Agent Venom, believing him to be his personal archnemesis.
Warren Ellis's newuniversal has John Tensen, a serial killer with psychic powers. His ability to see people's sins has led him to believe that he's dead and in hell, and that practically everyone deserves to die; and his ability to create blades of Hard Light has allowed him to embark on an endless killing spree.
Played around with in Punisher War Journal Annual #1 (2008)... the Big Bad's plot to siphon Frank Castle's psychosis and mind for sale as an intoxicant in gaseous form backfires when everyone exposed ends up "tripping" on the Punisher's mind... and the sheer messed-up-ness. The difference is that he is used to it even after he inhales his own psychosis and can still function, whereas the "super" wannabes that would have been barring his way become incapacitated, babbling wrecks. In general, some writers make him lean a bit in this direction, and the Punisher War Journal series has recently hinted at this.
Sin, the Red Skull's daughter, and her equally psychopathic boyfriend Crossbones. In modern Marvel the two are Mickey and Mallory Knox as supervillains, with all that entails. In their first story arc they go on a non-stop killing spree across America: Because they CAN.
Carnage from Spider-Man. He's the definition of an Ax Crazy, killing people and destroying things not because of any grand master plan on his part, but simply because he can. He's so much of an Ax Crazy that one of the most common manifestations of his ability to reform his arms into weapons is an ax. Not that he wasn't out of his gourd before bonding with the symbiote; he was a Serial Killer who had killed at least eleven people before being caught, and may have killed one or both of his parents.
Kimura, X-23's sadistic ex-handler at the Facility, who serves the same role for X-23 that Sabretooth does for Wolverine. Kimura took a special pleasure in torturing and both physically and emotionally abusing Laura, severely punished her even when she carried out her orders successfully, and has no qualms at all about killing anyone that potentially stands in the way of recapturing her. If they aren't in the way, she's perfectly willing to kill them anyway just because Laura cares for them. And when Kimura finally does recapture her, she goes to work on her with a chainsaw for "being a bad girl."
In American Vampire, you have Skinner Sweet...and quite a few of the more "traditional vampires," and Hattie's getting there in a hurry, if she isn't already there.
Archie Comics' Sonic the Hedgehog. Rosy the Rascal, the Mirror Universe version of Amy Rose, is Hammer Crazy. Like her counterpart, she used a magic ring to age herself up so that her beloved Sonic would finally notice her; unlike Amy, the ring drove her completely fuckin' nuts in the process and now she wants nothing more than to smash anything that breathes into a pulp.
From the same universe, "Super Scourge". While regular Scourge is just a more arrogant and cruel Sonic, Super Scourge is just non-stop violence and gleefully plans to destroy TWO whole planets. Because he CAN.
Similar things could be said of the incarnation of Super Sonic seen in the Fleetway (UK) Sonic the Comic. Except for the short period of time he had amnesia.
The Badger by Mike Baron featured a Badass Normal superhero... except that Norbert Sykes was in fact batshit insane with multiple personalities, one of which was his heroic alter ego, the Badger.
Evil Ernie of Chaos! Comics is Ax-Crazy, but for good reason. His childhood is horrific and the only people who try to "help" him are Mad Scientists. He eventually gets to pull the Ultimate Ax-Crazy Moment and kill the entire world..
Cain from Echo is genuinely insane, complete with religious delusions and messianic fantasies, and that only adds to the terror of his violent rampages. When a man is already mentally unstable things become worse when you add in the ability to fillet you with his mind.
All the villains in Hack/Slash. The essential concept of the series is that you can become undead just by being Ax Crazy enough, and it makes you worse.
Hothead Paisan: Homicidal Lesbian Terrorist. And bomb crazy, knife crazy, grenade crazy, baseball bat crazy, aerosol spray crazy...
Johnny: I've been talking to dead rabbits and feeding bloody walls. I've done horrifying things with salad tongs. It's really eaten into my social life.
The title character of Roman Dirge's comic Lenore the Cute Little Dead Girl is either Ax Crazy or a particularly dark and dangerous variation of a Cloudcuckoolander, depending on how generous one feels in their evaluation of her — although if one does consider her Ax Crazy, she's a very, very sympathetic portrayal of it.
Troy Grenzer in Shade, the Changing Man, the man who kills Kathy's parents. Subverted when Shade takes over his body at the point of his execution in the first issue. So the hero of the comic has the face and body of a convicted killer! Though Troy dies in the first issue, his influence is felt throughout the series.
The villainous Psyko, one of Sleepwalker's most dangerous adversaries, more than lives up to his name. He was a Serial Killerbefore being transformed into a demonic creature, and after that using his powers to make everyone else around him Brainwashed and Crazy, including Sleepwalker himself.
Subverted in the same series with the Chainsaw Vigilante, who was Exactly What It Says on the Tin... except he always fought to wound rather than kill (and was skilled enough with his weapon of choice to actually pull it off).
Galvatron, of Transformers, is frequently thought of as Ax Crazy. This is perhaps unfair. He is certainly insane—think Megatron, but (more?) operatic. He is not Ax Crazy, though...at first. His sanity degenerates markedly, seemingly after the destruction of Unicron, however; a popular Fanon theory wasn't quite made canon in Simon Furman's run on the G1 comics. By the end of the series (more accurately, the penultimate issue)...well, when you have a particle cannon that can blow apart even other creations of Unicron in a single shot, but think of this◊ as a good battlefield tactic, you have a good idea of how Galvatron thinks at this point...
There are two versions of Galvatron out of four (probably) who are legitimately crazy. The first Galvatron (the one from the UK comics) isn't crazy until his second appearance, where his head is scrambled by time-travel and a rough landing, but he tries to keep his sanity. Then Blaster shoots him with his electro-scrambler. He eventually recovers from that, for a time. Then he meets Megatron, and quickly goes right off the deep end.
The second Galvatron (the one from the US comics) manages to keep his sanity for a long while, up until he runs into a freshly revived Megatron. Then the Ark crashes into Earth, which really doesn't help. Galvatron spends the next several days wandering around Canada in a haze, but when Fortress Maximus attacks him, he finally snaps for good, and spends the last few minutes of his life in a berserk rage.
Then you have Straxus. The Decepticon warlord left in charge of Cybertron in the Marvel Comics, he's almost as insane as Galvatron. Bonus points for actually having an axe.
How about Menasor, the combined version of the Stunticons, who is a psychological mess due to two things; one, the five component parts have such extreme personalities (Dead End is a fatalist, Wildrider a psychopath, Breakdown a paranoid schizophrenic, Drag Strip a narcissist, and Motormaster a raging tyrant), and two, Motormaster is SUCH a raging tyrant that the other four utterly loathe him. And he likes it that way.
Megatron can veer into this. In issue 25 of the Marvel US series, he's so manic over the recent death of Optimus Prime that when Brawl, the most violent and bloodthirsty of the Combaticons, tries to be the voice of reason, Megatron crushes his cranial unit in with his bare hands! Brawl got better.
In the IDW continuity, Arcee went mad after Jhiaxus's experiments to reintroduce gender to Cybertron and hates him and everything associated with him. When Ultra Magnus apprehended her, she was sentenced to maximum security at Garrus-9, the separation of her spark; that period of isolation was the first time she felt at peace since her change. Her peace was broken when Fortress Maximus reconnected her so she could fight the Decepticon Secret Service when they raided the facility. She managed to track down Jhiaxus and spent six years repeatedly killing him. After Cybertron rebooted, Arcee became Prowl's secret enforcer.
No list of insane Transformers is complete without a mention of IDW's take on Overlord, who kicks this trope Up to Eleven and beyond.