Simon Petrikov as the Ice King. His homicidally dangerous and mentally unstable behavior is mostly due to his insanity and dementia thanks to the influence of his crown, with the Ice King being too insane to even know what he's really doing.
While Lemongrab is usually more weird and disturbed than dangerous, on his bad days he becomes dangerously unhinged and violent to the point of almost devouring his own brother. He is worse in "Too Old", becoming a completely Ax-Crazy dictator who is very open to sadism and senseless violence. Fortunately, he returns to being sympathetic once he is fused with his brother.
Flame Princess. Whether you think she is good or evil, it's clear she enjoys burning things a little too much, made abundantly clear after she goes on a rampage in "Vault of Bones".
Nicole Watterson. Several episodes have shown that she can become dangerously insane and even homicidal.
Though Ocho's explosive temper was previously established, in "The Uncle" he comes off as a psychotic delinquent who starts fights unprovoked, pretends to kidnap someone as a "prank", and was implied to have wanted Gumball to beat Darwin with a hammer just to prove his friendship with Ocho was more important.
In "The Deal", its revealed that Gumball, Darwin, and Anais become completely and utterly psychotic (to the point of frightening Nicole of all people) when theres nobody to keep them in line. They destroy everything in the house and try to launch the neighbor with a giant slingshot. Only Richard knows how to control them.
Barry Robinson, when he's not medicated. However, his true personality isn't completely held off by the meds. Even with his usual "simpleton" demeanor, he occasionally slips out a psychopathic thought or two.
Principal Brian Lewis, an ex-convict who has been shown drinking on the job, dealing drugs, assaulting students, and murdering more than a few people over the course of the show.
Arcane: Jynx as a teenager. Shes unpredictable to all, usually with explosive and/or deadly consequences.
Archer gives us Cheryl (who sometimes answers to "Carol", "Carina", "Cristal", and possibly a host of other names). She's a compulsive Pyromaniac, gets off on suffering physical and emotional violence, once spent 6 months believing that she was a werewolf, and is more often than not stoned out of her skull on either rubber cement or LSD-laced Gummi Bears (or both.) Luckily for everyone else at the company, she seems to get off more on her own pain than anyone else's. There's also Barry, who appears to have two personalities and has murdered several people, including the entire staff of a space station.
Around the end of Avatar: The Last AirbenderAzula definitely qualifies, having absolutely lost it after Mai and Ty Lee betrayed her. She has an absolute breakdown before her final battle with Zuko and Katara. Ozai also counts as this as while hes usually very self-controlled, if sadistic and short tempered, his glee at torching the Earth Kingdom in the climax shows just how much of a violent, sociopathic madman he is just inches beneath the surface.
Rampage of Beast Wars flips between this and a Blood Knight. Originally, he attempted to kill anything in sight, no matter whether they were Maximals or Predacons. In fact, the only reason he joined the Predacons after his first appearance was because Megatron held his life in his hands by removing his spark and keeping it for torture/incentive for Rampage to serve him, otherwise he'd probably try to kill them all. The fact he's one of the most heavily armed Transformers in the series doesn't help. He even mentions being a cannibal!
Dan Vs.: Dan himself, as well as many other characters he vows revenge on.
Danny Phantom has Danny's evilfutureself as this. The first thing he did upon "reawakening"? Steal the ghostly half of Big Bad Vlad Masters (Our Ghosts Are Different is in full force here) and then kill his human half in front of Vlad, who viewed Danny as a surrogate son. In his first scenes, he kills at least a dozen people as well and spends much of the episode killing or planning to kill some more. The fact that even Vlad refuses to tell Danny how his human half died speaks volumes.
Darkwing Duck's foe Negaduck is about as close to a kid-safe Ax Crazy as you can get, especially considering it's a Disney show. Negaduck's favored weapon, for example, is a chainsaw, and he takes great delight in attempting to blast cute fuzzy bunnies with a shotgun. This may or may not be a case of being a product of his environment.
Negaverse Launchpad? Happy with firing a bazooka at cute little girls. The Muddlefoot family? Tank's okay as a non-evil twin, but Herb, Binky, and Honker were shown with a row of severed duck heads on a pole in their yard. With their beaks sewn shut.
And let's not forget Darkwing's home grown supervillain, Quackerjack, who's just about as crazy as you could come (thought not nearly as crazy as Negaduck). He'll take any toy, make it dangerous, and use it to commit crimes of all sorts, not to mention he's constantly laughing at how much misfortune he's causing for others.
In Drawn Together , the mall policeman in the episode "The Lemon-AIDS Walk". At first he seems very relaxed, but suddenly points a gun at a woman and threatens to kill her if Wooldoor refused to throw some candy. When Wooldoor is captured, the policeman killed the women anyway just for the pleasure.
A number of the Drawn Together housemates qualify for this, with Captain Hero, who destroyed his home planet out of spite, being the most obvious.
Vicky. She's a crazed psychopath who will go above and beyond to torture kids For the Evulz.
Wanda. Specially when she is mad, demonstrates the sanity that she has, or rather, lacking. Not to mention she also demonstrates extremely sadistic tendencies. Especially in the episode "A Bad Case Of Diary-Uh!" when she finds out that Vicky called her a "fat pink squirrel".
In early seasons, Stewie was an extremely sadistic, deranged, homicidal baby psychopath obsessed with killing his mother, had a penchant for random violence, and did not hesitate to commit murder or torture if it brought him closer to his goals. He certainly has gotten saner and nicer over time, but it's still there.
Peter has shown multiple signs of being this in the later episodes.
Meg too, out of a desperation for love and affection, which is semi-Justified and understandable since she seldom receives love and affection.
Lois, when they ran out of paper towels on Christmas.
Stewie's evil clone, Evil Stewie, is a homicidal sadist who willingly commits torture and murder in his first few seconds on-screen. In many ways, he's like the Stewie Griffin of the first seasons, with all of his unbridled sadism and homicidal impulses intact.
Mac's personality goes from a very Nice Guy to completely lunatic if he gets even the smallest amount of sugar.
Wendell from Frisky Dingo is very definitely this. He randomly kills people for no conceivable reason, offers to abort a baby with a machete, then when said baby is born and revealed as a gigantic ant larvae monster, he rides it to the location of a doomsday device to destroy the Earth... just BECAUSE. With his pants off no less, commenting throughout on how wrong it is but how he's going to continue to do it.
Roberto, the dangerously insane, psychopathic robot whose literal function is to stab others (there's a reason he resembles a tombstone). His many insane acts includes robbing the same bank three times in a row, killing other robots to provide a disguise for himself, and "practicin' my stabbin"! Not that it's truly his fault; whatever idiot built him programmed him to be a sociopath.
Roberto: I'm thinking of a number between 1 and 10. Guess it, and you die first. Bender: Uh....56? Roberto: 56?? 56?! Now that's all I can think about! I'LL KILL YOU!
Then there's Robot Santa, who comes to kill people he considers naughty every Christmas, with his standard of what qualifies as "naughty" being ridiculously low.
Zoidberg's race go Ax Crazy during their mating season.
Harley Quinn (2019): Harley of course. As one might expect from the Joker's former top enforcer, she's short-tempered, unstable, and gleefully, eye-wateringly violent. As if to accentuate how violently insane she is, her happiest memory is apparently chopping one of her dolls' heads off with a cleaver when she was six.
Curly from Hey Arnold! is hinted to be this at times. Helga on occasion too, specifically in "Helga's Parrot".
Gaz also counts given she once happily used a device that could destroy the world and was disappointed when it failed to work. And then there's what she did to Iggins. Poor Iggins. He really should have listened to Gaz's warnings.
Dale Gribble is a bit of a mild example from this series. Dale is a major Conspiracy Theorist who thinks that everything and everyone is out to get him. He is also the most prone to threatening to kill others including his own friends and has been described as "mentally unstable" numerous times throughout the series. It doesn't help he's a professional exterminator and carries more guns than a regular person should need.
Mad Dog is basically Dale when he loses any small bit of sanity he has left. This dude is more prone to kill others when pushed too far (and that's a VERY thin line to cross) and even holds other people hostage when he doesn't get this way. You know you're crazy when it's Dale that has to be the one to save you.
Jimmy Whichard is definitely not right in the head. It's clear he's mentally unstable but is way more prone to violent outbursts than others.
However, the character that tops ALL of these characters above is Leanne Platter, Luanne's violent, alcoholic, jailbird mother. From having beaten up her ex-husband Hoyt every day while they were married to attacking her daughter's boyfriend with a fork after he rejects her advances to having an EXTREME Hair-Trigger Temper to literally pouncing on Peggy to making a mess wherever she goes, it's safe to say that's she's not entirely stable.
Ren himself. He's usually prone to psychotic fits of fury for little to no reason at times. He's even willing to kill anyone. This is not Played for Laughs in some episodes, however.
George Liquor, The Fire Chief and Haggis McHaggis as well.
Rick from Rick and Morty. He has been shown on multiple occasions to go absolutely berserk and overboard upon provocation, including ripping off the equivalent of a robot's testicles and shoving it down said robot's throat when tipped off to the police, engaging in cross-dimensional crossfire with himself when he thinks that other versions of him are trying to kill him, literally going Ax-Crazy and violently murdering various clones of himself (including a child and an infant), exploding an entire alien colonisation for putting him in a simulation and creating accurate genitalia for his grandson Morty, destroying an entire universe in order to spite its creator, programming his space-car to torture and murder in cruel and horrific ways or manipulate/coerce people into staying away from it when advised and committing countless other atrocities.
His daughter Beth is this as well, possibly even worse. As Rick puts it and gives her ample evidence of being Ax-Crazy:
"Bad father all the way to the max over here. Im a fucking nutcase. And the acorn plopped straight down, baby. Look at some of this shit you were asking me to make you as a kid. Ray guns, a whip that forces people to like you, invisibility cuffs, a parent trap, a lightning gun, a teddy bear with anatomically correct innards, night-vision googly-eye glasses, sound-erasing sneakers, false fingerprints, fall-asleep darts, a lie-detecting doll, an indestructible baseball bat, a taser shaped like a ladybug, a fake police badge, location-tracking stickers, rainbow-colored duct tape, mind-control hair clips, poison gum, a pink sentient switchblade."
Even his grandson Morty has shown shades of this: when he gets pushed and loses his sense of morality he becomes a homicidal lunatic.
Rocko's Modern Life: Rocko and Heffer are on a bus tour of Paris with a bus driver who is determined to keep his passengers on the bus at all costs, so much so that he chases them around the city after they escape.
Aku is a sadistic demon who commits carnage and torture for his own sick entertainment. In "Jack and the Zombies", he's very much the living embodiment of this trope. Notice his maniacal cackling while fighting Jack. During the beginning of the fight, Aku's laugh is absolutely psychotic, and then he goes on a murderous rampage.
Aku: "Oh Samurai? Where are you Sa-mu-rai? You can run but you cannot hide, CAUSE I CAN SMELL YOUR BLOOD!"
The High Priestess is the psychopathic leader of the Cult of Aku. Was the fact that she is the leader of a cult that worships the evolved form of a demonic entity, who abusively trains her seven daughters to be assassins of that entity any indication? When even Aku is surprised by her willingness to drink his essence, it says something about her insanity.
The Dominator, from "Episode XCVI", is a psychopathic man in Aku's employ who gleefully slaughtered an entire village just to start his plan. He's also an unbridled sadist to the point of getting off on enslaving children with audio frecuency and irrationally torturing Ashi for no reason.
Groundskeeper Willy is just one hair trigger away from becoming this trope.
Sideshow Bob started to qualify for this when his attempts to kill Bart included trying to have him cremated alive and when he visibly removed his cellmate's face and cut off his own. He also ties up Bart while singing casually about wanting to gouge out Bart's eyes. And then there's the "Treehouse of Horror XXVI" segment "Wanted: Dead, Then Alive" which has several moments that are genuinely disturbing. First, Sideshow Bob finally kills Bart. And it's not an over the top, comically ridiculous death, but fairly realistic. Bart gets harpooned through the heart, and since that doesn't immediately do the trick, Bob RETRACTS the harpoon and RIPS HIS HEART OUT. He then tears out Bart's large intestine and dances around with it while singing about how happy he is that Bart's dead before using it to tie his corpse to himself like a harness. It's also then revealed that Bob has kept Bart's corpse as it starts to decompose, eventually stuffing him in a compartment in the wall, even talking to him and playing golf with his body like he was alive. To make it worse, Bob revives Bart and then kills him again in various other ways — including getting him mauled by a lion and bludgeoning him with a sledgehammer while he's still conscious.
There was also a one-shot (well, technically, two-shot) character employed at the power plant in "Marge Gets A Job." This guy was shown polishing a shotgun and talking to himself:
Homer himself went on a murderous rampage in a "Treehouse of Horror" episode when the cable wasn't working and when they ran out of beer in a Whole Plot Reference to The Shining.
Homer: Well, what do you think, Marge? All I need is a title. I was thinking along the lines of "No TV and no beer make Homer go... something, something."
Marge: Go crazy?
Homer:DON'T MIND IF I DO!!!!(and proceeds to, well, go crazy)
Jack Lassen, Bart's substitute teacher from "Blazed and Confused", is a mentally unstable individual who burns a match on his eye, cuts himself with a knife just below his eye to scar himself, shaves Bart for attempting to pull a prank, electrocutes him, breaks things when angered, and finally tries to murder Bart for ruining his stint as the ignis for Blazing Guy. After getting fired from Springfield Elementary and getting a job at the penitentiary, he bonds with Sideshow Bob over their mutual murderous hatred of Bart.
In addition to Cartman, there is a good cast of violent, crazy characters: Saddam Hussein, the Earth Day Brainwashing Society, the Woodland Critters and Mickey Mouse. But Mel Gibson (in the canon of the series of course) is the best one.
Randy Marsh, especially in "T.M.I." and "A Nightmare on Facetime".
"Hell On Earth 2006" shows the "antics" of Ted Bundy, John Wayne Gacy and Jeffery Dahmer, Real LifeSerial Killers. Said "antics" are called so because they become a parody of sorts of The Three Stooges after their initial introduction.
The obviously insane Hat McCullough from "Free Hat", though his defenders claim he killed those twenty-three babies in self-defense.
Trent Boyett from "Pre-School". After he gets released from juvenile hall, he puts Butters and the sixth-graders in the hospital, the former for not coming to his defense when he was being arrested.
Mr. Krabs is often a step away from being dangerously insane because of his extreme obsession with money. "Clams", for instance, has SpongeBob and Squidward rightly disturbed from seeing him go crazy over Ol' Bluelips stealing his millionth dollar. This is even more prominent after the movie.
Mrs. Puff turned into this when she tried to murder SpongeBob in "Demolition Doofus"; when he did not get hurt in the demolition derby due to his Nigh-Invulnerability and bad driving and became a star instead, she's livid and tried to do it herself. And she does not get arrested for it. Toned down in the book release where she instead enters him in the derby in hopes he'll get badly injured to the point he'll never drive again.
Plankton himself became this in the first movie. He is much more deranged, sadistic, depraved and homicidal than usual.
Mr. Krabs in "Squeaky Boots" after SpongeBob's boots are hidden under the floorboards of the Krusty Krab, and he keeps hearing the squeaking sounds everywhere he looks.
In "Nature Pants", Patrick, of all people, goes crazy when SpongeBob refuses to come home. He even threatens to put SpongeBob in a jar and keep him in there. Forever.
SpongeBob himself becomes one in "Bummer Vacation" when he thinks Mr. Krabs is only putting him on vacation to replace him with Patrick, prompting him to strangle him and take his place.
Scarlet's true self is this. To the extent where she tried to blow up the island, which would have killed everyone.
Courtney is a more subtle version. While she starts out just a little uptight and arrogant, her unfair elimination in Island seems to have done a number on her sanity and from then on she seems to be extremely quick to resort to violence at the slightest inconvenience, and so obsessive that it comes across as somewhat divorced from reality. Heather even points out that she's become as unstable as Izzy following Courtney's boyfriend Duncan cheating on her with Gwen.
Josse, of the Ice Dancers from Total Drama Presents: The Ridonculous Race, is this. Aside from throwing temper tantrum just about every time she and her partner Jaques aren't in 1st place, she has no qualms about hurting people, even if the person in question is her own partner.