A great place to look is always Roger Ebert's 'Great Movies'! You can limit to release dates and genres if that's more to your liking. Some people have already given some great suggestions, but here are some I'd like to add (movies on the same line separated by slashes are by the same director(s)):
The Cabinet of Dr. Caligari
Battleship Potemkin
Steamboat Bill, Jr.
Un Chien Andalou / Bell du Jour / The Discreet Charm of the Bourgeoisie / The Exterminating Angel
Casablanca
Sunset Boulevard / The Apartment / Double Indemnity / Some Like It Hot / Ace in the Hole
The Big Sleep
Orpheus
All About Eve
Psycho / Rear Window / Vertigo / The Birds / Strangers on a Train
The Life of Oharu
Seven Samurai / Ran / Ikiru / Kagemusha
Monsieur Hulot's Holiday
Sweet Smell of Success
The 400 Blows / Jules and Jim / Day for Night
Cléo from 5 to 7
Laura
Last Year at Marienbad
Vivre Sa Vie / Breathless
Lawrence of Arabia
Network / 12 Angry Men / Dog Day Afternoon / Serpico
Au Revoir les Enfants
Solaris (1972) / Nostalghia / The Sacrifice
Tokyo Story / Late Spring / An Autumn Afternoon
The Seventh Seal / Persona / Fanny and Alexander (the 312 minute TV version) / Cries and Whispers / Autumn Sonata
8½ / La Dolce Vita / Amarcord / Fellini Satyricon
Three Colors trilogy (Blue / White / Red)
3 Women / The Long Goodbye / McCabe & Mrs. Miller / Nashville / Short Cuts
Badlands / Days of Heaven
The Godfather trilogy / Apocalypse Now / The Conversation
Woman in the Dunes / The Face of Another
Aguirre: The Wrath of God / The Enigma of Kaspar Hauser
Raging Bull / After Hours / Mean Streets / Taxi Driver / Casino / Goodfellas / The King of Comedy
Citizen Kane's already been mentioned, but I'd like to add Touch of Evil, F for Fake, The Magnificent Ambersons, and The Trial from Orson Welles! Also The Killing and Barry Lyndon from Stanley Kubrick! I'm not sure how narrow your view of classic is, but I hope this list is okay for now! I got tired and stopped *blush* THERE ARE TOO MANY—THIS IS A VERY INCOMPLETE LIST