Some Like It Hot - Everyone else has said it for me.
It Happened One Night - The best romantic comedy every. Clark Gable and Claudette Colbert are terrific in that.
A Streetcar Named Desire - Vivien Leigh and Marlon Brando gave the two best screen acting performances ever.
All About Eve - The dialogue is amazing, and when it's delivered by Bette Davis, even better.
Now, Voyager - I hate cigarette smoking in movies, but I'll admit it looks amazing in B&W. Another Bette Davis movie.
The Phildelphia Story - I'm getting teary eyed thinking about Katherine Hepburn, but she was just wonderful.
Clerks - OK, it's modern day, but it's shot in B&W. It makes me laugh so hard, and it reminds me of real life. It was Kevin Smith's first movie.