i dunno if anyone has mentioned these.. but you MUST watch this:
Amelie (le fabuleux destin d'Amelie Poulain).
it's seriously one of the most awesome (modern) movies ever.
You should also see at least a couple of Hayao Miyazaki's animated films. pure genius work.
some recommendations:
Princess Mononoke
Spirited Away
Nausicaä of the Valley of the Wind
here are some other suggestions. all of these were critically acclaimed, if you care about that sort of thing.
Schindler's List... this is a must.
Ray
To Kill a Mockingbird
Oldboy (Foreign - by a Korean director.)
Doctor Zhivago (classic film, historical context)
i sometimes check the if i don't know which dvds to rent. it's a pretty good guideline, i think, but not perfect.