I'd second
Sucker Punch. While the movie was barely watchable the soundtrack is GREAT. During the opening credits plays "When the Levee Breaks" (Led Zeppelin version) and later ... Just as
sarah-eats-cupcakes said, it's mostly (if not solely) covers, but really good ones - they are played completely differently than the originals. "Sweet Dreams" (Eurythmics, cover by Emily Browning), Search and Destroy (The Stooges cover by Skunk Anansie) and my absolute favorite "White Rabbit" (Jefferson Airplane covered by Emiliana Torrini).
The same -weak movie, great soundtrack - goes to the
Natural Born Killers, but for me because of a completely different reason than what
secretdesires said: for me it's not NIN but L7, Patti Smith (by the way she did also a great cover of White Rabbit on her album Twelve)...
The second one will not be a movie but a duet : composer and director. Meaning Elliott Smith (composer) and Gus Van Sant (director).
First movie that comes to mind would be
Elephant. about Columbine High School massacre. The soundtrack is mostly classical music, Beethoven's "For Elise" and "Moonlight Sonata" are combined into the story in such a way that gives you the creeps...
And in Paranoid Park and My Own Private Idaho you get to hear some of the Elliott Smith's songs: Angeles, White Lady..
When it comes to anime : sountracks by Yoko Kanno!