I guess I will post some of my favorites from teaching:
Ingmar Bergman: Fanny and Alexander, Persona, Smiles of a Summer Night, Autumn Sonata
Akira Kurosawa: Seven Samurai, Yojimbo, Ikiru, Ran, Dersu Uzalu
Federico Fellini: 81/2, the White Sheik, I Vitelloni, Amarcord
Francois Truffaut: Day for Night, The 400 Blows, The Last Metro, Jules et Jim, Shoot the Piano Player
Michelangelo Antonioni: L'Avventura, Blow-up, The Passenger
Ermanno Olmi: the Fiances, Il Posto, The Tree of Wooden Clogs
Bernardo Bertolucci: The Conformist, The Spider's Stratagem, The Last Emperor, Last Tango in Paris
Carne-Prevert: Children of Paradise
Robert Bresson: A Man Escaped, Mouchette
Vittorio De Sica: Garden of the Finzi-Continis, Bicycle Thieves, Umberto D.
Jean Renoir: Rules of the Game
Jacques Rivette: Celine and Julie Go Boating, La Belle Noiseuse
Werner Herzog: Aguirre, the Wrath of God, Stroszek, Grizzly Man, Land of Silence and Darkness
I'll stop there. Love film. By the way, Danny Boyle (dir. of Slumdog Millionaire) is the director of Trainspotting. I couldn't understand anything in that Scottish accent in the film.