Protectors of the Plot Continuum Agents have to be a little... strange... in order to function. However, some snap completely; this is called going flamethrower-crazy, as the most dramatic example involved a mad Agent tearing down the corridors with a flamethrower, looking to kill Mister Rogers, and anyone who got in his [the mad Agent's] way.
Tactical Noobs gives us the Crazy Burger King Guy, a Burger Fool who kills people for doing things like ordering food he cannot give them and voting for a different presidential candidate than him.
The protagonist Elsdon in Dusk Peterson's fantasy series The Eternal Dungeon.
While not as bad as, say, Ask That Guy with the Glasses or Sage, The Nostalgia Chick has a habit of smiling a big, girly grin right after she's said something disturbing. It kinda gives off the impression that she has more than a few screws loose.
And let's be honest here, while his craziness is different from Ask That Guy's stepford, sadistic brand, The Nostalgia Critic ain't exactly all there.
The actress playing Juliet in The Demented Cartoon Movie throws a bomb at her Romeo. After being told to not do it again, she goes crazy and throws a bomb at the replacement Romeo.
In the fan-made Zelda film Sage of Shadows, the True Villain, Davik, is fiendishly intelligent, and yet also a complete psychopath, poisoning his own sister and also gleefully murdering Link's parents in a very brutal fashion, as well as showcasing even after he lost his hand, and he plans on destroying the Cycle of Eternity due to psychopathic hatred of it. His voice actor, Michael Stevenson, has even stated that Davik is a villain comparable to The Joker in terms of mysteriousness and insanity.
Kevin "Aces" Low from New Game Plus The Rpg has become axe crazy due to his increasingly fragile mental state. He dispatches his planets minibosses with increasing violence, taken to using his powers to stalk his rival through a house, murdering his rivals followers as he goes, and burned out an imps eyes, all while wearing a Slasher Smile.
Hitler Rants and its spin-offs arguably has quite a few. The most extreme would have to be Mallory, who's Ax Crazy with dynamite. The only thing that makes it worse is that he is willing to do anything if it means blowing up Hitler.
Glove and Boots featured Jack Woods, who educates Mario and Fafa about raising a rabbit as a pet, and then how to butcher them... and then how to deal with zombie rabbits.
Worm has several, but the most extreme is probably Bakuda, a Mad Bomber who blows up her own subordinates for kicks.
Ultra Fast Pony has Derpy Hooves. The best example is her Day in the Limelight episode "Derp and Destruction", in which she gains supernatural powers and immediately decides to kill everyone in Ponyville with them. Of course, there were plenty of hints beforehand that she wasn't right in the head or safe: In "A Library with No Twilight", she has a brief scene attacking a tree branch while hurling curses at Mother Nature. And in "Ponynet Fight!" she drops heavy objects on Twilight's head and declares "You see, my way does work better!"