(A few notes: The cited release date is, as best I can tell, the first day a member of the general public could walk in off the street and buy a ticket to see the film, so festivals and premieres don't count. This only affected the chronological order in a few cases. Also, even less importantly, I composed this as a .txt document [because I'm an old, old person], so there are no diacritics over letters. Hence, I misspelled the names of a few directors, like Luis Buñuel.)
1. Broken Blossoms (5/13/19) (DW Griffith)
2. Safety Last! (4/1/23) (F Newmeyer)
3. The Thief of Bagdad (3/18/24) (R Walsh)
4. The Jazz Singer (10/6/27) (A Crosland)
5. Sunrise: A Song of Two Humans (9/23/27) (FW Murnau)
6. Frankenstein (11/21/31) (J Whale)
7. Freaks (2/20/32) (T Browning)
8. Grand Hotel (4/12/32) (E Goulding)
9. Trouble In Paradise (10/21/32) (E Lubitsch)
10. Footlight Parade (10/21/33) (10/21/33) (L Bacon)
11. Duck Soup (11/17/33) (L McCarey)
12. The Thin Man (5/25/34) (WS Van Dyke)
13. Mutiny on The Bounty (11/8/35) (F Lloyd)
14. A Night At The Opera (11/15/35) (S Wood)
15. Modern Times (2/5/36) (C Chaplin)
16. Grand Illusion (6/8/37) (J Renoir)
17. The Life of Emile Zola (8/11/37) (W Dieterle)
18. You Can't Take It With You (9/1/38) (F Capra)
19. Bringing Up Baby (11/23/38) (H Hawks)
20. Stagecoach (3/3/39) (J Ford)
21. Ninotchka (11/9/39 (E Lubitsch)
22. His Girl Friday (1/11/40) (H Hawks)
23. The Grapes of Wrath (1/24/40) (J Ford)
24. Rebecca (4/12/40) (A Hitchcock)
25. The Great Dictator (10/15/40) (C Chaplin)
26. The Bank Dick (11/29/40) (E Cline)
27. The Philadelphia Story (12/26/40) (G Cukor)
28. The Lady Eve (2/25/41) (P Sturges)
29. How Green Was My Valley (10/28/41) (J Ford)
30. Sullivan's Travels (1/15/42) (P Sturges)
31. To Be Or Not To Be (2/19/42) (E Lubitsch)
32. Yankee Doodle Dandy (5/29/42) (M Curtiz)
33. Mrs. Miniver (6/2/42) (W Wyler)
34. Cat People (12/25/42) (J Tourneur)
35. Shadow Of A Doubt (1/12/43) (A Hitchcock)
36. Meet Me In St. Louis (11/28/44) (V Minnelli)
37. Mildred Pierce (9/28/45) (M Curtiz)
38. The Lost Weekend (11/29/45) (B Wilder)
39. The Big Sleep (8/23/46) (H Hawks)
40. Out of the Past (11/25/47) (J Tourneur)
41. The Third Man (9/1/49) (C Reed)
42. Adam's Rib (11/18/49) (G Cukor)
43. Sunset Boulevard (8/10/50) (B Wilder)
44. A Place in the Sun (8/14/51) (G Stevens)
45. The Day The Earth Stood Still (9/18/51) (R Wise)
46. Umberto D (1/20/52) (V de Sica)
47. Shane (4/23/53) (G Stevens)
48. La Strada (9/22/54) (F Fellini)
49. The Night of the Hunter (7/26/55) (C Laughton)
50. War and Peace (8/21/56) (K Vidor)
51. Around The World in 80 Days (10/17/56) (M Todd)
52. Paths of Glory (12/25/57) (S Kubrick)
53. Touch of Evil (4/23/58) (O Welles)
54. Mon Oncle (5/10/58) (J Tati)
55. Gigi (5/15/58) (V Minnelli)
56. The 400 Blows (5/4/59) (F. Truffaut)
57. Hiroshima Mon Amour (6/10/59) (A Resnais)
58. La Dolce Vita (2/5/60) (F Fellini)
59. The Manchurian Candidate (10/24/62) (J Frankenheimer)
60. To Kill A Mockingbird (12/25/62) (R Mulligan)
61. The Shop on Main Street (10/8/65) (J Kadar)
62. Butch Cassidy & The Sundance Kid (10/24/69) (GR Hill)
63. Patton (4/2/70) (F Schaffner)
64. The French Connection (10/9/71) (W Friedkin)
65. Harold And Maude (12/20/71) (H Ashby)
66. Cabaret (2/13/72) (B Fosse)
67. The Discreet Charm of the Bourgeoisie (9/15/72) (L Bunuel)
68. American Graffiti (8/11/73) (G Lucas)
69. Mean Streets (10/14/73) (M Scorcese)
70. Amarcord (12/18/73) (F Fellini)
71. All The President's Men (4/9/76) (A Pakula)
72. That Obscure Object of Desire (8/17/77) (L Bunuel)
73. Get Out Your Handkerchiefs (1/11/78) (B Blier)
74. The Tin Drum (5/3/79) (V Schlondorff)
75. Apocalypse Now (8/15/79) (FF Coppola)
76. Atlantic City (9/3/80) (L Malle)
77. Return of the Secaucus Seven (9/5/80) (J Sayles)
78. Ordinary People (9/19/80) (R Redford)
79. Pixote (9/26/80) (H Babenco)
80. Blade Runner (6/25/82) (R Scott)
81. Gandhi (11/30/82) (R Attenborough)
82. Hannah And Her Sisters (2/7/86) (W Allen)
83. Platoon (12/19/86) (O Stone)
84. Broadcast News (12/16/87) (JL Brooks)
85. The Story Of Women (2/15/88) (C Chabrol)
86. Women On The Verge of A Nervous Breakdown (11/11/88) (P Almodovar)
87. Cinema Paradiso (11/17/88) (G Tornatore)
88. Do The Right Thing (7/21/89) (S Lee)
89. The Freshman (7/20/90) (A Bergman)
90. Dances With Wolves (11/6/90) (K Costner)
91. The Double Life of Veronique (5/15/91) (K Kieslowski)
92. Raise The Red Lantern (9/91) (Z Yimou)
93. The Last of The Mohicans (8/26/92) (M Mann)
94. The Story of Qiu Ju (9/92) (Z Yimou)
95. The Crying Game (10/30/92) (N Jordan)
96. Farewell My Concubine (1/1/93) (Chen/Kaige)
97. Forrest Gump (7/6/94) (R Zemeckis)
98. Babe (8/4/95) (C Noonan)
99. Leaving Las Vegas (10/27/95) (M Figgis)
100. Fargo (3/8/96) (Coens)
If you feel like buying any of these films, please consider using this link. I'll get a few pennies if you do, to help me buy all the films I don't already own. Thanks!