We watch a lot of classic movies, so it would be really hard for me to narrow it down to a top three, but three I do really enjoy and watch whenever I can are:
Casablanca - because I love the performances of Ingrid Bergman, Humprhey Bogart, and Claude Rains
A Room with a View - because I love those Merchant-Ivory dramas and Italy, too
My Cousin Vinny - because Joe Pesci, Fred Gwynne, and Marissa Tomei are outstandingly funny, and it was apparently Fred Gwynne's last movie
Gretchen