I took a drama class where we basically watched a lot of the "basics" I guess.
These are the films I remember that I don't think has been mentioned yet: Psycho, Butch Cassidy and the Sundance Kid, The Graduate, Rain Man, It's a Wonderful Life, The Sting... that's about all I can remember that's not been mentioned yet.
I don't know too much about film and whatnot but the class pretty much centered around the classics. I remember watching Mr. Smith Goes to Washington and really liking that one, too. I guess that's just taste, though. I'm a sucker for sappy stuff sometimes =(
Also China Town. That's a good noir film.