I decided to make this as a kind of alternative to the Academy Award for Best Picture list, merely for my own amusement. The awards for Best Director and Best Picture are related, but fundamentally different. Over 25% of the films that have been awarded Best Picture were not awarded Best Director.

The Best Director award is awarded for excellence in cinematic direction by exclusive vote of the Academy's Directing branch. The award obviously goes to the director.

The Best Picture award is awarded for the overall quality of production by vote of the entire Academy. The award goes to the producer.

The Best Picture award had an interesting start. There was no Best Picture award at the 1st Academy Awards, instead two separate production awards were handed out. One was the Most Outstanding Production award, which went to Wings (William A. Wellman, 1927), and one was the Most Artistic Quality of Production award, which went to Sunrise (F. W. Murnau, 1927). At the 2nd Academy Awards the latter award was scrapped, and the surviving award for Most Outstanding Production was simply renamed Best Production (and eventually renamed Best Picture). That means that the Best Picture award itself always looks to overall commercial production quality rather than artistic quality (for which there is no longer an award). It also means that Sunrise did not win Best Picture.

Because of the difference between the two awards when Best Director and Best Picture awards go to separate films there can be a bit of controversy. For example Rebecca (Alfred Hitchcock, 1940) won Best Picture, but Hitchcock himself was never awarded Best Director. Occasionally the Best Director award goes to a film that didn't even get a Best Picture nomination, or vice versa. I've listed all the times that a disparity between the Best Picture award and Best Director award occurred.

BEST DIRECTOR VS. BEST PICTURE
1927/28 (#1-#2)
D: 7th Heaven (Frank Borzage, 1927) + Two Arabian Knights (Lewis Milestone, 1927)*
P: Wings (William A. Wellman, 1927)*

1928/29 (#3)
D: The Divine Lady (Frank Lloyd, 1929)*
P: The Broadway Melody (Harry Beaumont, 1929)

1930/31 (#5)
D: Skippy (Norman Taurog, 1931)
P: Cimarron (Wesley Ruggles, 1931)

1931/32 (#6)
D: Bad Girl (Frank Borzage, 1931)
P: Grand Hotel (Edmund Goulding, 1932)*

1935 (#9)
D: The Informer (John Ford, 1935)
P: Mutiny on the Bounty (Frank Lloyd, 1935)

1936 (#10)
D: Mr. Deeds Goes to Town (Frank Capra, 1936)
P: The Great Ziegfeld (Robert Z. Leonard, 1936)

1937 (#11)
D: The Awful Truth (Leo McCarey, 1937)
P: The Life of Emile Zola (William Dieterle, 1937)

1940 (#14)
D: The Grapes of Wrath (John Ford, 1940)
P: Rebecca (Alfred Hitchcock, 1940)

1948 (#22)
D: The Treasure of the Sierra Madre (John Huston, 1948)
P: Hamlet (Laurence Olivier, 1948)

1949 (#23)
D: A Letter to Three Wives (Joseph L. Mankiewicz, 1949)
P: All the King's Men (Robert Rossen, 1949)

1951 (#25)
D: A Place in the Sun (George Stevens, 1951)
P: An American in Paris (Vincente Minnelli, 1951)

1952 (#26)
D: The Quiet Man (John Ford, 1952)
P: The Greatest Show on Earth (Cecil B. DeMille, 1952)

1956 (#30)
D: Giant (George Stevens, 1956)
P: Around the World in 80 Days (Michael Anderson, 1956)

1967 (#41)
D: The Graduate (Mike Nichols, 1967)
P: In the Heat of the Night (Norman Jewison, 1967)

1972 (#46)
D: Cabaret (Bob Fosse, 1972)
P: The Godfather (Francis Ford Coppola, 1972)

1981 (#55)
D: Reds (Warren Beatty, 1981)
P: Chariots of Fire (Hugh Hudson, 1981)

1989 (#63)
D: Born on the Fourth of July (Oliver Stone, 1989)
P: Driving Miss Daisy (Bruce Beresford, 1989)*

1998 (#72)
D: Saving Private Ryan (Steven Spielberg, 1998)
P: Shakespeare in Love (John Madden, 1998)

2000 (#74)
D: Traffic (Steven Soderbergh, 2000)
P: Gladiator (Ridley Scott, 2000)

2002 (#76)
D: The Pianist (Roman Polanski, 2002)
P: Chicago (Rob Marshall, 2002)

2005 (#79)
D: Brokeback Mountain (Ang Lee, 2005)
P: Crash (Paul Haggis, 2005)

2012 (#85)
D: Life of Pi (Ang Lee, 2012)
P: Argo (Ben Affleck, 2012)*

*Indicates that this film was not nominated in the other category.

NOTES
There were two Best Director awards handed out at the 1st Academy Awards.
#1 7th Heaven (Frank Borzage, 1927) won Best Dramatic Direction.
#2 Two Arabian Knights (Lewis Milestone, 1927) won Best Comedic Direction.