Lists of "bests" are generally neither very interesting or very durable. I happened to hear a fairly large selection of the "special" on the TOP 100 SONGS FROM U.S. FILMS and was somewhat impressed by how many actually were good songs. The thought that appears is "How many of these will be "Folk" music in another 50 years or so?". (Or how many are now?)
While ordinarily a link would serve better, I don't have one yet, and I suspect that this, like other similar lists, will fade pretty quickly – along with most of the links that will appear soon.
So for what it's worth, here's the American Film Institute's list as printed by the Wichita (Kansas) Eagle newspaper, June 23, 2004.
Shown as Song Title, with the movie name and year of release of the movie.
1. Over the Rainbow The Wizard of Oz 1939
2. As Time Goes by Casablanca 1942
3. Singin' in the Rain Singin' in the Rain 1952
4. Moon River Breakfast at Tiffany's 1961
5. White Christmas Holiday Inn 1942
6. Mrs. Robinson The Graduate 1967
7. When You Wish Upon a Star Pinocchio 1940
8. The Way We Were The Way We Were 1973
9. Stayin' Alive Saturday Night Fever 1977
10. The Sound of Music The Sound of Music 1965
11. The Man That Got Away A Star Is Born 1954
12. Diamonds Are a Girl's Best Friend Gentlemen Prefer Blondes 1953
13. People Funny Girl 1968
14. My Heart Will Go On Titanic 1997
15. Cheek to Cheek Top Hat 1935
16. Evergreen (Love Theme - A Star Is Born) A Star Is Born 1976
17. I Could Have Danced All Night My Fair Lady 1964
18. Cabaret Cabaret 1972
19. Some Day My Prince Will Come Snow White & the Seven Dwarfs 1937
20. Somewhere West Side Story 1961
21. Jailhouse Rock Jailhouse Rock 1957
22. Everybody's Talkin' Midnight Cowboy 1969
23. Raindrops Keep Fallin' on My Head Butch Cassidy/Sundance Kid 1969
24. 0l' Man River Show Boat 1936
25. High Noon (Do Not Forsake Me, Oh My Darlin') High Noon 1952
26. The Trolley Song Meet Me in St. Louis 1944
27. Unchained Melody Ghost 1990
28. Some Enchanted Evening South Pacific 1958
29. Born to Be Wild Easy Rider 1969
30. Stormy Weather Stormy Weather 1943
31. Theme From New York, New York New York, New York 1977
32. I Got Rhythm An American in Paris 1951
33. Aquarius Hair 1979
34. Let's Call the Whole Thing Off Shall We Dance 1937
35. America West Side Story 1961
36. Supercalifragilistic-expialidocious Mary Poppins 1964
37. Swinging on a Star Going My Way 1944
38. Theme From 'Shaft,' Shaft 1971
39. Days of Wine and Roses Days of Wine and Roses 1963
40. Fight the Power Do the Right Thing 1989
41. New York, New York On the Town 1949
42. Luck Be a Lady Guys and Dolls 1955
43. The Way You Look Tonight Swing Time 1936
44. Wind Beneath My Wings Beaches 1988
45. That's Entertainment The Band Wagon 1953
46. Don't Rain on My Parade Funny Girl 1968
47. Zip-a-Dee-Doo-Dah Song of the South 1947
48. Whatever Will Be, Will Be (Que Sera, Sera) The Man Who Knew Too Much 1956
49. Make 'Em Laugh Singin' in the Rain 1952
50. Rock Around the Clock Blackboard Jungle 1955
51. Fame Fame 1980
52. Summertime Porgy and Bess 1959
53. Goldfinger Goldfinger 1964
54. Shall We Dance The King and I 1956
55. Flashdance … What a Feeling Flashdance 1983
56. Thank Heaven for Little Girls Gigi 1958
57. The Windmills of Your Mind The Thomas Crown Affair 1968
58. Gonna Fly Now Rocky 1976
59. Tonight West Side Story 1961
60. It Had to Be You When Harry Met Sally 1989
61. Get Happy Summer Stock 1950
62. Beauty and the Beast Beauty and the Beast 1991
63. Thanks for the Memory The Big Broadcast of 1938 1938
64. My Favorite Things The Sound of Music 1965
65. I Will Always Love You The Bodyguard 1992
66. Suicide Is Painless M*A*S*H* 1970
67. Nobody Does It Better The Spy Who Loved Me 1977
68. Streets of Philadelphia Philadelphia 1993
69. On the Good Ship Lollipop Bright Eyes 1934
70. Summer Nights Grease 1978
71. The Yankee Doodle Boy Yankee Doodle Dandy 1942
72. Good Morning Singin' in the Rain 1952
73. Isn't It Romantic? Love Me Tonight 1932
74. Rainbow Connection The Muppet Movie 1979
75. Up Where We Belong An Officer and a Gentleman 1982
76. Have Yourself a Merry Little Christmas Meet Me in St Louis 1944
77. The Shadow of Your Smile The Sandpiper 1965
78. 9 to 5 9 to 5 1980
79. Arthur's Theme (Best That You Can Do) Arthur 1981
80. Springtime for Hitler The Producers 1968
81. I'm Easy Nashville 1975
82. Ding Dong the Witch Is Dead The Wizard of Oz 1939
83. The Rose The Rose 1979
84. Put the Blame on Mame Gilda 1946
85. Come What May Moulin Rouge! 2001
86. (I've Had) The Time of My Life Dirty Dancing 1987
87. Buttons and Bows The Paleface 1948
88. Do Re Mi The Sound of Music 1965
89. Puttin' on the Ritz Young Frankenstein 1974
90. Seems Like Old Times Annie Hall 1977
91. Let the River Run Working Girl 1988
92. Long Ago and Far Away Cover Girl 1944
93. Lose Yourself 8 Mile 2002
94. Ain't Too Proud to Beg The Big Chill 1983
95. (We're Off on the) Road to Morocco Road to Morocco 1942
96. Footloose Footloose 1984
97. 42nd Street 42nd Street 1933
98. All That Jazz Chicago 2002
99. Hakuna Matata The Lion King 1994
100. Old Time Rock and Roll Risky Business 1983