If you've only seen the remake you need to see this campy original. It's a real slice of Cold War fear, but the kids will dig it because of Gort the robot.
Jaws is considered to be the first summer blockbuster, and if you've never seen it in all it's bloody glory on the big screen, you should. And it's free.
It's a little tough to call this movie a "classic" because I always think of classic movies as something from the 30s or 40s, but A Little Romance is a classic movie.
I've only seen it once because I can't do all those dead people, but friends who have seen it more than once tell me they can't unsee Bruce as a dead guy.