Nowhere near complete, but here goes...
M (1931): dir. Fritz Lang
Bride of Frankenstein (1935): dir. James Whale
The Maltese Falcon (1941): dir. John Huston
Rope (1948): dir. Alfred Hitchcock
The Treasure of the Sierra Madre (1948): dir. John Huston
The Third Man (1949): dir. Carol Reed
Rashomon (1950): dir. Akira Kurosawa
The Wages of Fear (1953): dir.Henri-Georges Clouzot
Seven Samurai (1954): dir. Akira Kurosawa
Rififi (1955): dir. Jules Dassin
The Searchers (1956): dir. John Ford
Paths of Glory (1957): dir. Stanley Kubrick
Throne of Blood (1957): dir Akira Kurosawa
Psycho (1960): dir. Alfred Hitchcock
The Hustler (1961): dir. Robert Rossen
The Manchurian Candidate (1962): dir. John Frankenheimer
Dr. Strangelove (1964): dir. Stanley Kubrick
The Good, The Bad and The Ugly (1966): dir. Sergio Leone
Bonnie and Clyde (1967): dir. Arthur Penn
Point Blank (1967): dir. John Boorman
Night of the Living Dead (1968): dir. George Romero
Midnight Cowboy (1969): dir. John Schlesinger
The Godfather (1972): dir. Francis Ford Coppola
High Plains Drifter (1973): dir. Clint Eastwood
One Flew Over the Cuckoo's Nest (1975): dir. Milos Forman
Taxi Driver (1976): Martin Scorcese
Animal House (1978): dir. John Landis
Halloween (1978): dir. John Carpenter
This is Spinal Tap (1984): dir. Rob Reiner
House of Games (1987): dir. David Mamet
Grave of the Fireflies (1988): dir. Isao Takahata
Reservoir Dogs (1992): dir. Quentin Tarantino
Hana-Bi (1997): dir. Takeshi Kitano
Audition (1999): dir. Takashi Miike
Amelie (2001): dir. Jean-Pierre Jeunet
Millennium Actress (2001): dir. Satoshi Kon
If you made it all the way to the bottom of this list, you're probably wondering why none of the Star Wars movies are listed. It's nothing personal against George Lucas - even he would say if you want to learn about film making, you should immerse yourself in the films of Akira Kurosawa. His 1958 film "The Hidden Fortress" was a big influence on Star Wars.
I didn't leave "Silence of the Lambs" out by accident, either. Fritz Lang's "M" was one of the first serial killer/police procedural movies, as well as one of the first "talkies" to integrate sound as a vital plot element. Don't let black & white and foreign films put you off - there's a whole world of great films out there.
I listed "Rififi" because it's one of the first "Heist" movies - any film that depicts a daring heist shown in intricate detail owes a debt to "Rififi"; alas, it's due for a remake in 2011.
Thanks for reading.