Here's a quick list of movies of various sorts you really should see at some point in your life, for various reasons. :)

Movies you've probably never heard of

Alphaville - French scifi, very haught style, experimental feel.
Carnosaur - The earth *was* made for the dinosaurs, darnit. :)
Dark Star - John Carpenter meets Alien, how can you go wrong?
The Flower of My Secret - From the maker of 'Women on the Verge of a Nervous Breakdown'
Nausicaa, of the Valley of the Winds - Miyazaki's masterpiece. 'Nuff said.
Plague Dogs - Good if you're in the mood for incredibly depressing cartoons
Pterodactyl Woman from Beverly Hills - A rather Dadaistic take on monster movies
Ratboy - Horrid film, but amusing to sit through :)
Schizopolis - Surrealistic comedy at its best; very entertaining.
Tampopo - Japanese noodle meets spaghetti western
Twenty Bucks - Following a bill through a city

Really cool movies more akin to public consumption

The Adventures of Baron Munchausen - A delightful Gilliam work.
Adventures of Buckaroo Banzai Across the 8th Dimension - Kicks ass. :)
Better Off Dead - Savage Steve Holland is so very funny!
Contact - True to the book; amazing!
eXistenZ - Cronenberg film. Okay, this one didn't hold up over the years.
Fear and Loathing in Las Vegas - Trippy fun.
The Fifth Element - Kicks ass.
The Hudsucker Proxy - Probably my favorite Coen Bros movie
The Iron Giant - This work of art deserves all the attention it can muster.
L.A. Story - LA, talking signs, love. One of my very favorites.
The Player - He gets away with it!
Pulp Fiction - I want a briefcase for my soul, too.
The Secret of NIMH - What animation should be. Though they should have stuck to the ending in the book.
Tank Girl - Not the greatest of films, but hey, still lots of fun.
Until the End of the World - neat study of near-future society, with a story that twists and turns through all sorts of interesting things

A special treat

Mr Garfield Goes to Hollywood - a wonderful NPR segment about the movie industry