Personal favorites that haven't yet been mentioned (that I've seen):
-The pianist: In-friggin'-credible. Just an amazing movie, Adrian Brody spent 3 months learning to play Chopin and losing weight just to play this role. Really a must-watch piece of cinema that will blow every other movie you've watched about the Holocaust right out of the water.
-Eternal Sunshine of a Spotless Mind (beautiful movie, really moving)
-Requiem for a Dream (most powerful anti-drug work I've ever witnessed, and nowhere in the movie is the word "heroin" ever said or written)
-Punch-Drunk Love: A really cooky movie, presents the mindset of the main character really well, and lets you get in his head. Also if you want to see Adam Sandler do serious acting, it's a great example.
-V for Vendetta: Bad-ass to the core, and really incredible in its messages+themes
-Das Boot: An unbelievable piece of German cinematography, showing the life of German soldiers on a U-Boat from their perspective. Great Foreign film, very very different from American movies. It doesn't spell everything out for you, and it's really about making you feel specific emotions, and it does a wonderful job of that. Don't watch it if you only like happy endings or are claustrophobic.
-Phonebooth: pyschological thriller, I found it riveting and fascinating
-The Professional: Great French cinema, hitman adopts a 12-year old girl. Lots of explosions+shooting and human interactions.
-Amelie: Fairly typical of French cinematography, a LOT of references will go right over your head (only works in French), but a thoroughly enjoably, adorable movie.
-Chicago/Cabaret: If you like musicals, you'll probably love these
-Mouline Rouge: Same. A lot like Amelie in the way that it's very standard and straightforward, but well executed and a pleasure to watch. Interesting use of modern music to make the main character appear to everyone else as a musical genius.
-Godfather I and II (I wouldn't recommend III): For some reason, these movies turned out amazing.
-Silence of the Lambs: One of the most absolutely faithful adaptations of a book into cinema that I've ever seen. Read the book first, and you'll see that almost every scene is in the book and they don't cut corners. Very well done, Anthony Hopkins portrays Hannibal Lector brilliantly.