Of the ones I have seen. The best are Godfather 1 and 2, Bridge on the River Kwai, Lawrence of Arabia, Casablanca (GOAT), Schindler's List, Annie Hall
The worst of the ones I have seen Crash, Gladiator, Rain man, Slumdog Millionaire, Silence of the Lambs, Amadeus.
French Connection and Midnight Cowboy have dated terribly. You can tell some years where there was no standout so a really popular and generally well made film wins. Nothing outright terrible has won. There's no best picture oscar for Battle of the Five Armies, Phantom Menace, Last Action Hero or the like.
2014 - "Birdman"
2012 - "Argo"
2011 - "The Artist"
2010 - "The King's Speech"
2009 - "The Hurt Locker"
2008 - "Slumdog Millionaire"
2007 - "No Country for Old Men"
2006 - "The Departed"
2005 - "Crash"
2003 - "The Lord of the Rings: The Return of the King"
2000 - "Gladiator"
1999 - "American Beauty"
1998 - "Shakespeare in Love"
1997 - "Titanic"
1995 - "Braveheart"
1994 - "Forrest Gump"
1993 - "Schindlers List"
1992 - "Unforgiven"
1991 - "The Silence of the Lambs"
1988 - "Rain Man"
1986 - "Platoon"
1984 - "Amadeus"
1982 - "Gandhi"
1981 - "Chariots of Fire"
1977 - "Annie Hall"
1976 - "Rocky"
1975 - "One Flew over the Cuckoo's Nest"
1974 - "The Godfather Part II"
1973 - "The Sting"
1972 - "The Godfather"
1971 - "The French Connection"
1970 - "Patton"
1969 - "Midnight Cowboy"
1965 - "The Sound of Music"
1962 - "Lawrence of Arabia"
1957 - "The Bridge on the River Kwai"
1943 - "Casablanca"
1939 - "Gone with the Wind"