Most videogames require the player to overcome a trial, to defeat an overarching enemy. In order to make the enemy seem as inhuman as possible to drive the player's need to hand a smackdown to the big bad, the opponent is often painted with a stroke of the insanity brush. Sometimes it works; sometimes it doesn't.
Here are the ones I feel did it.
Kefka Palazzo FFVI
Um... If someone were to explain Kefka's insanity, they would need little evidence beyond his clownish appearance. When you get past that, you can appreciate just how sociopathic he is: just because he doesn't want to wait, he poisons an entire kingdom's water supply; he is fond of jumping around the screen like a hyper baby; and then he has the laugh, the first bit of spoken dialogue in a Final Fantasy game.
Dr. J.S. Steinman Bioshock
In a game showing off the most morally corrupt examples of humanity who often skirt the line between sanity and insanity, the good doctor ran over the line, kept going, and never looked back. While he does not play an important role in the plot of the game, Steinman is owner of one of the most disturbing scenes in the entire game. You watch as he mercilessly kills a Splicer by performing a surgery while she is conscious and ranting about how she won't hold still long enough for him to make her beautiful. Then he sets his eyes upon you and you know you have stared insanity in the face.
Mitsuo Kubo Persona 4
This one is probably known only by Persona and SMT fans. Mitsuo is a low key character throughout most of the game, until the party suspects him of being the serial killer throwing people into the TV world. And when they come across him and his shadow in said world, Chie even remarks that she does not know which one is the shadow. And when it comes out that *SPOILER* he was a copy cat killer who wanted to use the murders to make himself feel important*SPOILER* you get the sense of just how unhinged he is. Then there is the fact that his part of the TV world is set in a game and his shadow is a baby with an old-school 8-bit warrior shell showing that he has no real mental capabilities and that his view of the world is little more than a game he is interacting in.
Albedo Xenosaga series
This is a guy who finds pleasure in tearing off his own arm and head to frighten a little girl, kills all of his followers for practically no reason at all, and uses the Bible as a source of menacing quotes. This isn't exactly your typical JRPG villain. And his laugh is even more unnerving than Kefka's, believe it or not.
Gary Smith Bully
While neither a murderer nor a world-destroying baddie, Gary is included because his actions are horribly common. His sociopathic tendencies include lying, bribery, and manipulation. No matter how horrible his behaviour, he is never affected by it because he doesn't see any of the people around him as people. They are just things to be used to raise his own status. This is something that any person could be capable of and are all telltale signs of a much deeper damage of the psyche. Plus, the guy dresses as a Nazi for Halloween.