Tier 1:
Drama: The Shawshank Redemption
American Beauty
Whisper of the Heart
Biography/Drama: Jarhead
Crime/Drama: Lord of War
Sci-Fi: A Clockwork Orange
Blade Runner
Action: Batman Begins
Spirited Away
Tier 2:
Action: Pirates of the Caribbean: The Curse of the Black Pearl
Princess Mononoke
Gladiator
Sci-Fi: Children of Men
Drama: My Neighbor Totoro
Tier 3:
Drama: Gandhi
One Flew Over the ****oo's Nest
Hotel Rwanda
Syriana
Crime/Drama: The Silence of the Lambs
Pulp Fiction
Sci-Fi: Metropolis
Have more if you need them, but those are enough to get you started. The only films on this list pre 90's are Blade Runner (80's), Clockwork Orange (70's I believe) and Metropolis (20's). And Gandhi and Whisper of the Heart are 80's I believe, but the latter is animated anyways. While Metropolis may be too much of a turnoff because of age Blade Runner and Clockwork are musts, and you will not care when they were made once you see them. Enjoy. Films are one of my favorite hobbies!