More Mel:
-Young Frankenstein. In b&w, for the feel of an old-time movie.
-Blazing Saddles. Warning--the "n" word is thrown a LOT, but it's actually a pretty progressive movie. And most of people using it are the bad guys.

Along with the Hitchcock films agentpompadour recommended below, I'd like to specifically add:
-Rope. It's awesome.
-Psycho. It deserves every bit of its reputation as a classic.

Wizard of Oz. I saw this a few years ago and was amazed at how well it still holds up.

The original Gojira. NOT the American move Godzilla: King of the Monsters, the original, Japanese version. There's a huge difference between the two.

Have you see any Kurosawa Akira, like Rashomon or The Seven Samurai?