Radiohead
Now that I have your attention, frankly I couldn't watch the movie with its original soundtrack. It just felt too melodramatic. To make it sound edgy, I watched it with Radiohead's Kid A playing in the background and never did I feel that the movie went out of sync. Towards the end I saw it with In Rainbows playing in the background which again wasn't bad either.
Let me know if you have ever tried this and what music you used.
Please share your experiences in case you have done something similar with this movie.