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Underground:

http://www.imdb.com/title/tt0114787/

Its the story of a people, a humanist film made from love and borne out of grief.

House of Flying Daggers?!?! I'd give that film like 1/5

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That's probably my favorite movie of all time.

Others mentioned that I think are great: In the Mood For Love, The Lives of Others, Amelie, A Very Long Engagement, Amores perros and Raise the Red Lantern.

Not so great in my opinon: Y tu mamá también, Battle Royale and Ran

A bunch of asian movies mentioned that I haven't seen yet but would like to eventually.

Some of my favorites:

Festen/The Celebration

The City of Lost Children

Anything by Kieslowski who hasn't been mentioned yet, especially of course his Trois couleurs trillogy.

Europa

Lilja 4-ever

Some may not enjoy him but I'm gonna say almost anything by Almodovar as well. Especially: Carne Tremula and Hable con ella

Tierra

Au revoir, les enfants

Tesis

Delicatessen

Fear X

and some Michael Haneke movies: Caché which is the most accessible and La Pianiste and Code inconnu as well.