As we've established, "favorite" and "Greatest" are different, so I think the greatest are:

Broken Blossoms (Griffith)
Vertigo (Hitchcock)
Touch of Evil (Welles)
Pierrot Le Fou (Godard)
The Searchers (Ford)
2001: A Space Oddyssey (Kubrick)
Battleship Potemkin (Eisenstein)
The Gold Rush (Chaplin)
La Dolce Vita (Fellini)
Schindler's List (Spielberg)
Raging Bull (Scorsese)
Ran (Kurosawa)
The Seventh Seal (Bergman)
Lawrence of Arabia (Lean)
The Third Man (Reed)
Some like it Hot (Wilder)
Grand Illusion (Renoir)
The Godfather (Coppola)
His Girl Friday (Hawks)
Jules and Jim (Truffaut)
The General (Keaton)
Metropolis (Lang)
A Man Escaped (Bresson)
Singing in the Rain (Donen)
Belle De Jour (Bunuel)
Trouble in Paradise (Lubistch)