I considered mentioning Donnie Darko but it's unclear whether he's mentally ill or if something supernatural/sci-fi-ish is actually going on.
Yeah, I always thought there was a greater possibility that he was prey to some freakish supernatural event than just being screwy but it does feature some therapy sessions, hypnotherapy etc. I guess, in a pretty cynical fashion though.
K-Pax is another excellent call, I read the books and loved the movie but I'm pretty sure that he is meant to be an alien as opposed to some mad guy, in both stories, on screen and in the book.
United States of Tara. Not a movie, but an award-winning black humor/drama TV series that lasted 3 years: Toni Collette stars as a wife and mother with Multiple Personality Disorder. The first season is kind of playful with the subject; seasons 2 and 3 turn considerably darker. The TV series was written by Diablo Cody (she also wrote the move “Juno”).
“There are two novels that can change a bookish fourteen-year old’s life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs.” ~ John Rogers