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Why 1940? Mostly because that's where the Wikipedia entry starts. The history of the award is a little muddled, with name changes, combinations and divisions with other awards, etc. I needed a logical starting point, and Wikipedia chose for me, so there you have it.
In case you're curious, here's the list from which I'm working:
1940: The Great McGinty (Preston Sturges)
1941: Citizen Kane (Herman Mankiewicz, Orson Welles)
1942: Woman of the Year (Michael Kanin, Ring Lardner, Jr.)
1943: Princess O'Rourke (Norman Krasna)
1944: Wilson (Lamar Trotti)
1945: Marie-Louise (Richard Schweizer)
1946: The Seventh Veil (Muriel Box, Sydney Box)
1947: The Bachelor and the Bobby-Soxer (Sydney Sheldon)
1949: Battleground (Robert Pirosh)
1950: Sunset Boulevard (Charles Brackett, D.M. Marshman, Jr., Billy Wilder)
1951: An American in Paris (Alan Jay Lerner)
1952: The Lavender Hill Mob (T.E.B. Clarke)
1953: Titanic (Charles Brackett, Richard Breen, Walter Reisch)
1954: On the Waterfront (Budd Schulberg)
1955: Interrupted Melody (Sonya Levien, William Ludwig)
1956: The Red Balloon (Albert Lamorisse)
1957: Designing Woman (George Wells)
1958: The Defiant Ones (Nathan E. Douglas, Harold Jacob Smith)
1959: Pillow Talk (Clarence Greene, Maurice Richlin, Russell Rouse, Stanley Shapiro)
1960: The Apartment (I.A.L. Diamond, Billy Wilder)
1961: Splendor in the Grass (William Inge)
1962: Divorce, Italian Style (Ennio de Concini, Pietro Germi, Alfredo Giannetti)
1963: How the West Was Won (James Webb)
1964: Father Goose (Peter Stone, Frank Tarloff)
1965: Darling (Frederic Raphael)
1966: A Man and a Woman (Claude Lelouch [story]; Claude Lelouch, Pierre Uytterhoeven [screenplay])
1967: Guess Who's Coming to Dinner (William Rose)
1968: The Producers (Mel Brooks)
1969: Butch Cassidy & the Sundance Kid (William Goldman)
1970: Patton (Francis Ford Coppola, Edmund H. North)
1971: The Hospital (Paddy Chayefsky)
1972: The Candidate (Jerry Larner)
1973: The Sting (David S. Ward)
1974: Chinatown (Robert Towne)
1975: Dog Day Afternoon (Frank Pierson)
1976: Network (Paddy Chayefsky)
1977: Annie Hall (Woody Allen, Marshall Brickman)
1978: Coming Home (Robert C. Jones, Waldo Salt [screenplay]; Nancy Dowd [story])
1979: Breaking Away (Steve Tesich)
1980: Melvin and Howard (Bo Goldman)
1981: Chariots of Fire (Colin Welland)
1982: Gandhi (John Briley)
1983: Tender Mercies (Horton Foote)
1984: Places in the Heart (Robert Benton)
1985: Witness (William Kelley, Earl Wallace [screenplay]; William Kelley, Pamela Wallace, Earl Wallace [story])
1986: Hannah and Her Sisters (Woody Allen)
1987: Moonstruck (John Patrick Shanley)
1988: Rain Man (Ronald Bass, Barry Morrow)
1989: Dead Poets Society (Tom Schulman)
1990: Ghost (Bruce Joel Rubin)
1991: Thelma and Louise (Callie Khouri)
1992: The Crying Game (Neil Jordan)
1993: The Piano (Jane Campion)
1994: Pulp Fiction (Quentin Tarantino [story and screenplay] and Roger Avary [story])
1995: The Usual Suspects (Christopher McQuarrie)
1996: Fargo (Ethan and Joel Coen)
1997: Good Will Hunting (Ben Affleck, Matt Damon)
1998: Shakespeare in Love (Marc Norman and Tom Stoppard)
1999: American Beauty (Alan Ball)
2000: Almost Famous (Cameron Crowe)
2001: Gosford Park (Julian Fellowes)
2002: Talk to Her/Habla con Ella (Pedro Almodóvar)
2003: Lost in Translation (Sofia Coppola)
2004: Eternal Sunshine of the Spotless Mind (Charlie Kaufman, Michel Gondry, and Pierre Bismuth)
2005: Crash (Paul Haggis and Bobby Moresco)
2006: Little Miss Sunshine (Michael Arndt)
2007: Juno (Diablo Cody)
I'm going to try to get through at least one of these a week, and I'm also going to try to post some sort of analysis of each film. I figure this will force me to actively analyze these movies as opposed to just sitting back and watching them without any critical thought. Should be a good academic experience, and hopefully I'll be able to use some of what I learn to improve my own writing.