A lot ('The Social Network'!) of the experts ('The King's Speech'!) are obsessed ('The Fighter'!) with what will happen ('Inception'!) on Oscar night. ('Black Swan'!) Personally, I think it's much more interesting to look back and see what already has happened. And by using the magic of numbers, combined with the invaluable assistance of Wikipedia, I've come up with some rather amusing little tidbits. (Some of these you may have read before, but oh well. They're still cool.)
1a. 'The Lord of the Rings: Return of the King' (2003) won 11 Oscars out of 11 nominations. Statistically speaking, it's the king of the Oscar heap. Other 100% winners include 'Gigi' (1958) and 'The Last Emperor' (1987), both of which went 9 for 9, and 'It Happened One Night' (1934), which was 5 for 5.
1b. 'The Matrix' (1999) won 4 out of 4, and the 3 for 3 club includes 'The Bourne Ultimatum' (2007), 'Grand Prix' (1966), and 'Jurassic Park' (1993). Several films have gone 2 for 2 and 1 for 1, but that's not all that interesting, plus it's too much research.
2. Only one film has ever won Best Picture and nothing else. It was 'The Broadway Melody' (1929), and its other nominations were for Best Director (Harry Beaumont) and Best Actress (Bessie Love). (Correction! 'Grand Hotel' (1932) also won Best Picture and nothing else ... because that was its only nomination!)
3. The 1956 short film 'The Red Balloon' won an Oscar for Best Original Screenplay, despite having zero dialogue.