Rather than repeating some of those already mentioned that I thoroughly enjoyed, I'll add a few that -- somewhat surprisingly -- have not been mentioned.
Love and Death -- Woody Allen's version of the great Russian novels.
Pocketful of Miracles -- combination romantic comedy/gangster movie by Frank Capra. Ann Margaret isn't that impressive, and overall not one of the best, but I give it extra credit for Bette Davis as well as great character actors like Thomas Mitchell, Peter Falk, Arthur O'Connell, and Edward Everett Horton.
The Cheap Detective -- Peter Falk in a Neil Simon parody of Bogey. Although I enjoy Neil Simon, I rarely include his movies among the best, but this is one of my favorites of all time. You may never been able to watch
Casablanca,
The Maltese Falcon,
The Big Sleep,
To Have and Have Not, etc. with a straight face again.