I really like "Harvey". It was released in 1950 and stars James Stewart as a nice fellow whose best friend just so happens to be a six-foot tall rabbit. A very well-dressed rabbit, might I add.
"One Flew Over the Cuckoo's Nest" is one of my favorite films as well-of those involving mental illness and not.
Oh, and "Fisher King".
I am quite a fan of horror films as well. All of which, undoubtedly, include a character with some form of mental instability.