Non-American Films I recommend
Angel-A
City of Lost Children
Let the Right One In
The Killer
Hard Boiled
Raise the Red Lantern
Shanghai Triad
The Emperor and the Assassin is awesome.
For Westerners who are curious about anime,
Cowboy Bebop, the Movie
Wings of Honneamise (a bit dense, but whoooboy, the animation)
And lately,
The Devil's Double