kottke.org linked to a film critic's list of 102 movies you must see to be considered "movie-literate." I don't think it's necessary to see every single film on the list, I think if there are some you haven't seen you can make up for it by having seen some other greats not on the list. But I agree with his basic premise that if you haven't seen most of them, it's a lot harder for you to have a literate discussion with others about film.
Kottke went through it and made Kottke's list of the 102 "essential" movies he has seen. He's seen 40. I went through the list myself and found I've seen 86 of them. Many I saw in film classes I took as electives in college. A few, like Aguirre, the Wrath of God and Singin' in the Rain (how's that for a double-feature?), I was forced to watch by my now-spouse (didn't like Aguirre, liked Singin'). A few I haven't seen I had to look up to make sure I knew what they were. For instance I thought Days of Heaven was "that Terrence Malick film" but I wasn't sure. I had never heard of the W.C. Fields film, It's a Gift before seeing this list. I don't think I've ever seen an entire W.C. Fields movie, I suppose that's a gap in my knowledge but I've never had much appreciation for him.
My list is below the jump. The plus signs (+) are ones I've seen, the asterisks (*) are ones Kottke has seen. Sorry they're not all linkified but the original article has links to Roger Ebert reviews for every one. I can understand not ever watching old french films but how can someone in their 30s (I think that's his age range) have missed seeing Jaws on TV at some point? Nevermind that it's awesome.
+* 2001: A Space Odyssey * The 400 Blows +8 1/2 +Aguirre, the Wrath of God +* Alien +All About Eve +* Annie Hall +* Apocalypse Now +* Bambi +The Battleship Potemkin The Best Years of Our Lives +The Big Red One The Bicycle Thief +The Big Sleep +* Blade Runner +Blowup +* Blue Velvet +Bonnie and Clyde +Breathless +Bringing Up Baby +Carrie +* Casablanca +Un Chien Andalou Children of Paradise / Les Enfants du Paradis +* Chinatown +* Citizen Kane +* A Clockwork Orange +* The Crying Game +The Day the Earth Stood Still Days of Heaven +* Dirty Harry +The Discreet Charm of the Bourgeoisie +* Do the Right Thing +La Dolce Vita +Double Indemnity +* Dr. Strangelove +Duck Soup +* E.T. -- The Extra-Terrestrial +Easy Rider +* The Empire Strikes Back +The Exorcist +* Fargo +* Fight Club +Frankenstein The General +* The Godfather, The Godfather, Part II +* Gone With the Wind +* GoodFellas +* The Graduate +Halloween * A Hard Day's Night Intolerance It's a Gift +* It's a Wonderful Life +Jaws +The Lady Eve +Lawrence of Arabia +M +Mad Max 2 / The Road Warrior +The Maltese Falcon +* The Manchurian Candidate +Metropolis +Modern Times +* Monty Python and the Holy Grail +Nashville +The Night of the Hunter +Night of the Living Dead +* North by Northwest +* Nosferatu +* On the Waterfront +Once Upon a Time in the West Out of the Past +Persona Pink Flamingos +Psycho +* Pulp Fiction +Rashomon +* Rear Window +Rebel Without a Cause +Red River Repulsion +The Rules of the Game +* Scarface The Scarlet Empress +* Schindler's List The Searchers +* The Seven Samurai +Singin' in the Rain +Some Like It Hot A Star Is Born +A Streetcar Named Desire +Sunset Boulevard +* Taxi Driver +The Third Man +Tokyo Story +* Touch of Evil +The Treasure of the Sierra Madre Trouble in Paradise +Vertigo +* West Side Story +The Wild Bunch +* The Wizard of Oz