Top Dog Meme from lordjubatus
I'm too lazy to italicize them as is proper, so I'll use that for the ones I've seen to differentiate them from the title bar. I'm sure you can guess how this works as easily as I did.
Best Picture Winners:
1928-Wings/Sunrise
1929-The Broadway Melody
1930-All Quiet on the Western Front
1931-Cimarron
1932-Grand Hotel
1933-Cavalcade
1934-It Happened One Night
1935-Mutiny on the Bounty
1936-The Great Ziegfield
1937-The Life of Emile Zola
1938-You Can't Take It with You
1939-Gone with The Wind
1940-Rebecca
1941-How Green Was My Valley
1942-Mrs. Miniver
1943-Casablanca
1944-Going My Way
1945-The Lost Weekend
1946-The Best Years of Our Lives
1947-A Gentleman's Agreement
1948-Hamlet
1949-All the King's Men
1950-All about Eve
1951-An American in Paris
1952-The Greatest Show on Earth
1953-From Here to Eternity
1954-On the Waterfront
1955-Marty
1956-The King and I
1957-Bridge on the River Kwai
1958-Gigi
1959-Ben Hur
1960-The Apartment
1961-West Side Story
1962-Lawrence of Arabia
1963-Tom Jones
1964-My Fair Lady
1965-The Sound of Music
1966-A Man for All Seasons
1967-In the Heat of the Night
1968-Oliver
1969-Midnight Cowboy
1970-Patton
1971-The French Connection
1972-The Godfather
1973-The Sting
1974-The Godfather Part 2
1975-One Flew Over the Cuckoo's Nest
1976-Rocky
1977-Annie Hall
1978-The Deer Hunter
1979-Kramer vs. Kramer
1980-Ordinary People
1981-Chariots of Fire
1982-Gandhi
1983-Terms of Endearment
1984-Amadeus (a good proportion, but audio only to avoid having to get another actor to play the freighter captain)
1985-Out of Africa
1986-Platoon (×2)
1987-The Last Emperor
1988-Rain Man
1989-Driving Miss Daisy
1990-Dances with Wolves
1991-Silence of the Lambs
1992-Unforgiven
1993-Schindler's List
1994-Forrest Gump
1995-Braveheart
1996-The English Patient
1997-Titanic
1998-Shakespeare in Love
1999-American Beauty
2000-Gladiator (×!)
2001-A Beautiful Mind (×2)
2002-Chicago
2003-Lord of the Rings: The Return of the King (×3)
2004-Million Dollar Baby
2005-Crash
2006-The Departed
2007-No Country for Old Men
Total: 10/81 (altered from 79 because there are supposedly 80 of them, and one had two awards that were later rolled into one)
Incidentally, the two oldest movies that I've seen in full (as far as I know) were also nominees for '39. I'm sure you can guess which those were.