Too many of the films that came to mind immediately have already been mentioned, so I'll just second those, before I mention a couple that no one else has listed yet.
So an enthusiastic second to:
These are among my favorite movies of any genre:
Quatermass and the Pit (when I saw it, it was called 5 Million Years to Earth)
The Day the Earth Stood Still
Galaxy Quest
And then there are:
Invaders From Mars (original), although I like the American ending better than the UK ending
Metropolis
Silent Running
War of the Worlds (original)
When Worlds Collide
Star Wars (the original three films only)
LotR
As for my contributions:
Science-fiction: The Blob (original), which is not great film-making, but it's fun, it touches all the right bases. And it has Steve McQueen in it.
Fantasy: Field of Dreams. Yes, they sold it as a baseball movie. And it is that. But it is even more than that a fantasy film, and a very, very good one. I think it gets short shrift as a fantasy because it takes place in the present, more or less in the real world, and it has sports in it.