There are so many movies that I like it is impossible to list them all. I checked
AFI's top 100 and here are the ones on their list I like.
2. CASABLANCA (1942)
3. THE GODFATHER (1972)
5. LAWRENCE OF ARABIA (1962)
6. THE WIZARD OF OZ (1939)
9. SCHINDLER'S LIST (1993)
11. IT'S A WONDERFUL LIFE (1946)
13. THE BRIDGE ON THE RIVER KWAI (1957)
15. STAR WARS (1977)
17. THE AFRICAN QUEEN (1951)
20. ONE FLEW OVER THE CUCKOO'S NEST (1975)
21. THE GRAPES OF WRATH (1940)
23. THE MALTESE FALCON (1941)
25. E.T. THE EXTRA-TERRESTRIAL (1982)
29. MR. SMITH GOES TO WASHINGTON (1939)
32. THE GODFATHER PART II (1974)
33. HIGH NOON (1952)
34. TO KILL A MOCKINGBIRD (1962)
35. IT HAPPENED ONE NIGHT (1934)
40. NORTH BY NORTHWEST (1959)
42. REAR WINDOW (1954)
49. SNOW WHITE AND THE SEVEN DWARFS (1937)
50. BUTCH CASSIDY AND THE SUNDANCE KID (1969)
51. THE PHILADELPHIA STORY (1940)
53. AMADEUS (1984)
55. THE SOUND OF MUSIC (1965)
56. M*A*S*H (1970)
60. RAIDERS OF THE LOST ARK (1981)
62. TOOTSIE (1982)
63. STAGECOACH (1939)
69. SHANE (1953)
71. FORREST GUMP (1994)
72. BEN-HUR (1959)
75. DANCES WITH WOLVES (1990)
77. AMERICAN GRAFFITI (1973)
78. ROCKY (1976)
86. MUTINY ON THE BOUNTY (1935)
89. PATTON (1970)
97. BRINGING UP BABY (1938)
99. GUESS WHO'S COMING TO DINNER (1967)
100. YANKEE DOODLE DANDY (1942)
From their 10th Anniversary list:
50. THE LORD OF THE RINGS: THE FELLOWSHIP OF THE RING (2001)
71. SAVING PRIVATE RYAN (1998)
72. THE SHAWSHANK REDEMPTION (1994)
77. ALL THE PRESIDENT'S MEN (1976)
81. SPARTACUS (1960)
87. 12 ANGRY MEN (1957)
There are a lot of other movies I like. Three Days of the Condor; The Sting; A lot of animated pictures. In cue on my dvr I have: The Big Sleep; The Dirty Doz; Where Eagles Dare; Secretariat; The Time Machine; The Quiet Man; The Pink Panther; For Love of the Game; Now You See Me 1 & 2; The Man Who Shot Liberty Valance; Mister Roberts; Key Largo; Captains Courageous; Friendly Persuasion; Red Tails; 42; 61; Tomorrowland; Good Will Hunting; I Remember Momma and Flags of Our Fathers