Movie character, suddely became obsessive/crazy

You could check out Field of Dreams.

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I may go back to hating you. It was more fun.

This probably doesn't fit the model that AMHmovie was looking for, but this thread reminded me of the movie Falling Down (1993) where Michael Douglas plays a man who completely unravels over the course of the film. It's tragic because, on some level, most of us can relate to the many little things that frustrate the character and help lead to his ultimate breakdown (of course there's a little more to it than hamburgers not looking like they do in the photos at fast food restaurants or the price of a soda).
Douglas' character becomes obsessed with simply "going home,", but encounters problems along the way.

Taxi Driver
Scarface (well, sorta at the end guy is TOTALLY out of his mind)
The Believer
The Abyss
M
Fatal Attraction (maybe)
MaCbeth (1971, Polanski)
2001:A Space Odyssey
A Woman Under the Influence
The Deer Hunter (Walken character)
Aguirre:Wrath of God
The Machinist
Black Swan (bad copy of Repulsion)
Pi
Vertigo
Repulsion

It took me a second, when you mentioned 2001... but I assume you were talking about Hal. Which is really a great example. Despite Hal being a machine, he does gradually become paranoid and obsessed over his mission, even to the point of murder.

Haven't seen several of these, but The Machinist is another good one that fits the bill... (but in a very dark way).

A very obvious character, though I didn't see him above, Frodo. He becomes obsessed with the One Ring because it controls him. We can actually feel sad for his character because of the way that the Ring mistreats him. Though he is not psychopathic or whatever, if you're looking for great performances, check it out (it is more than possible that you've already seen it)

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Overall...[Rocket_Sam]

Yes. Hal 9000 and Dave Bowman. At the end of movie we see Dave as old man still haunted by mission...