Several of my all-time favourites have been mentioned already, including North by Northwest, Casablanca and The Seventh Seal (Say, when you hear the name Bergman, do you immediately think of Ingrid or Ingmar?
)
Way too many to list fully, but a selection of my other favourites includes:
Some Like it Hot
Duck Soup
The African Queen
The Third Man
Seven Samurai
Rashomon
Stalag 17
Breakfast at Tiffany's
Dr. Strangelove
It's a Mad, Mad, Mad, Mad World
Damn Yankees
The Manchurian Candidate