"One Flew Over the Cuckoo's Nest" is another good movie. Then there's that one with Angelina Jolie in it... "Girl, Interrupted". I love "Don Juan DeMarco" ... it has Johnny Depp in it.

It's funny too. Another movie is one people have probably heard of - "Sybil". I thought it was very interesting, but it's dramatic, not funny.
There's also that set of moves about Hannibal Lecter. The first one has the guy that plays Gil Grissom on CSI. Then there's Hannibal, Red Dragon, and Silence of the Lambs. It's a bit freaky set of movies though, but fulfills the "psychological" aspect because of the presence of a psychologist.
----------
Here is an awesome site listing different movies and mental illnesses that they portray.
Movies and Mental Illness Filmography