"Casablanca" hands down. It's just so perfect. The characters, the intrigue, the romance, the humor, the music are all just so... perfect.
And it has such perfect dialogue, such as...
Casablanca (1942)
Ilsa: Who is Rick?
"Well, Rick is the kind of man that... well, if I were a woman, and I were not around, I should be in love with Rick. But what a fool I am talking to a beautiful woman about another man."