For the posts expounding on these choices:
Introduction
#1-5 #6-15 #16-25 #26-35 #36-45 #46-55
#56-65 #66-75 #76-85 #86-95 #96-105 #106-115
Notable omissions
1. The Passion of Joan of Arc (Dreyer, 1928)
2. Tokyo Story (Ozu, 1953)
3. Sunrise: A Song of Two Humans (Murnau, 1927)
4. Vertigo (Hitchcock, 1958)
5. Seven Samurai (Kurosawa, 1954)
6. PlayTime (Tati, 1967)
7. The Rules of the Game (Renoir, 1939)
8. Citizen Kane (Welles, 1941)
9. Persona (Bergman, 1966)
10. The General (Keaton, 1926)
11. Ran (Kurosawa, 1985)
12. Casablanca (Curtiz, 1942)
13. City Lights (Chaplin, 1931)
14. Brief Encounter (Lean, 1945)
15. Night and Fog (Resnais, 1955)
16. The Third Man (Reed, 1949)
17. Cries and Whispers (Bergman, 1972)
18. Viridiana (Buñuel, 1961)
19. Singin’ in the Rain (Donen & Kelly, 1952)
20. Contempt (Godard, 1963)
21. Three Colors Trilogy (Kieślowski, 1993-’94)
22. Man with a Movie Camera (Vertov, 1929)
23. Ugetsu (Mizoguchi, 1953)
24. Jeanne Dielman, 23 Quai du Commerce, 1080 Bruxelles (Akerman, 1975)
25. The Searchers (Ford, 1956)
26. Andrei Rublev (Tarkovsky, 1966)
27. Ordet (Dreyer, 1955)
28. Some Like It Hot (Wilder, 1959)
29. 2001: A Space Odyssey (Kubrick, 1968)
30. Earth (Dovzhenko, 1930)
31. 8½ (Fellini, 1963)
32. Rashomon (Kurosawa, 1950)
33. Duck Amuck (Jones, 1953)
34. A Woman Under the Influence (Cassavetes, 1974)
35. Band of Outsiders (Godard, 1964)
36. The Passenger (Antonioni, 1975)
37. Sansho the Bailiff (Mizoguchi, 1954)
38. The Crowd (Vidor, 1928)
39. Le million (Clair, 1931)
40. Lawrence of Arabia (Lean, 1962)
41. M (Lang, 1931)
42. Late Spring (Ozu, 1949)
43. The Trial (Welles, 1962)
44. Once Upon a Time in the West (Leone, 1968)
45. Raging Bull (Scorsese, 1980)
46. The Last Laugh (Murnau, 1924)
47. The Double Life of Véronique (Kieślowski, 1991)
48. Pinocchio (Luske & Sharpsteen, 1940)
49. The Battle of Algiers (Pontecorvo, 1966)
50. Psycho (Hitchcock, 1960)
51. Barry Lyndon (Kubrick, 1975)
52. Sherlock Jr. (Keaton, 1924)
53. Annie Hall (Allen, 1977)
54. Spirit of the Beehive (Erice, 1973)
55. Stagecoach (Ford, 1939)
56. Paris, Texas (Wenders, 1984)
57. Cléo from 5 to 7 (Varda, 1962)
58. Nashville (Altman, 1975)
59. L’avventura (Antonioni, 1960)
60. The Earrings of Madame de… (Ophuls, 1953)
61. Aguirre, the Wrath of God (Herzog, 1972)
62. Grand Illusion (Renoir, 1937)
63. Sunset Blvd. (Wilder, 1950)
64. Sans soleil (Marker, 1983)
65. North by Northwest (Hitchcock, 1959)
66. The Bridge on the River Kwai (Lean, 1957)
67. Vampyr (Dreyer, 1932)
68. The Marriage of Maria Braun (Fassbinder, 1979)
69. M. Hulot’s Holiday (Tati, 1953, France)
70. A Matter of Life and Death (Powell & Pressburger, 1946)
71. Revenge of a Kinematograph Cameraman (Starewicz, 1912)
72. The Apu Trilogy (Ray, 1955-’59)
73. What’s Opera, Doc? (Jones, 1957)
74. In the Mood for Love (Wong, 2000)
75. Koyaanisqatsi (Reggio, 1982)
76. Brazil (Gilliam, 1985)
77. The Lady Eve (Sturges, 1941)
78. Park Row (Fuller, 1952
79. Black Narcissus (Powell & Pressburger, 1947)
80. La strada (Fellini, 1954)
81. She Wore a Yellow Ribbon (Ford, 1949)
82. Steamboat Willie (Iwerks, 1928)
83. The Mother and the Whore (Eustache, 1973)
84. The Ascent (Shepitko, 1977)
85. Short Cuts (Altman, 1993)
86. Pierrot le fou (Godard, 1965)
87. Badlands (Malick, 1973)
88. The Piano (Campion, 1993)
89. Le samouraï (Melville, 1967)
90. Fast, Cheap & Out of Control (Morris, 1997)
91. Blade Runner (Scott, 1982)
92. Winter Light (Bergman, 1963)
93. Laura (Preminger, 1944)
94. Day for Night (Truffaut, 1973)
95. Duck Soup (McCarey, 1933)
96. Au hasard Balthazar (Bresson, 1966)
97. The Conversation (Coppola, 1974, USA)
98. F for Fake (Welles, 1973)
99. His Girl Friday (Hawks, 1940)
100. Jaws (Spielberg, 1975)
101. All About My Mother (Almodóvar, 1999)
102. Hiroshima mon amour (Resnais, 1959)
103. Fantasia (Disney Animation Studios, 1940)
104. Yi yi (Yang, 2000)
105. Angels with Dirty Faces (Curtiz, 1938)
106. The Gold Rush (Chaplin, 1925)
107. Suspiria (Argento, 1977)
108. Solaris (Tarkovsky, 1972)
109. The Umbrellas of Cherbourg (Demy, 1964)
110. The Damned (Visconti, 1969)
111. La jetée (Marker, 1962)
112. Chungking Express (Wong, 1994)
113. Secrets & Lies (Leigh, 1996)
114. The Godfather & The Godfather, Part II (Coppola, 1972/1974)
115. Gerald McBoing-Boing (Cannon, 1951)