These are my favorite (not the best. . .necessarily) movies from The Criterion Collection. Of course, they have hundreds of other great films too; I just haven't seen them (yet).
Grand Illusion - Jean Renoir (one of the great great movies...one notch under [or over] Citizen Kane)
Seven Samurai - Kurosawa (a three hour long epic film)
The 400 Blows - Francois Truffaut
This Is Spinal Tap - Rob Reiner (one of my top five knucklehead movies)
The Long Good Friday - John McKenzie
M - Fritz Lang - an awesome thriller
Nanook of the North - killer early documentary. Sorry, Frank Zappa didn't invent Nanook.
Time Bandits - Terry Gilliam (esp. if you're a Gilliam fan)
Henry V - Laurence Olivier (one of the best Shakespeare movies ever)
Fishing with John - John Lurie (a very funny and strange sort of travelogue, with Jim Jarmusch, Tom Waits, and Willem DaFoe)
Brazil - Terry Gilliam (This movie is one of a kind)
The Harder They Come - Perry Henzell (and dark, and very cool plunge into Shantytown, Reggae, and Rasta, with a great soundtrack)
The Blob - The classic spooky movie
Do the Right Thing - Spike Lee (his best movie, I think)
Playtime - Jacque Tati (I wonder if I would still like Tati movies?)
8 1/2 - Federico Fellini
Monterey Pop Festival (Hendrix, Joplin, Otis Redding and others broke out)
3 Women - Robert Altman
Slacker - Richard Linklater (an Austin movie--people seem to love it or hate it; the second time I saw it, everyone in the room fell asleep)
The Life Aquatic with Steve Zissou - Wes Anderson (my favorite Wes movie)
Murmur of the heart - Louis Malle
Dazes and Confused - Richard Linklater
Stranger than paradise - jim jarmusch
Traffic - Jacques Tati
The Discreet Charm of the Bourgeoisie - Luis Buñuel
Spartacus- Stanley Kubrick
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[see, also, A List of Lists on All This Is That]