Rufus Wainwright - Hallelujah, Leonard Cohen (best version of all that are out there IMO - timing is impeccable; his version was on The Shrek Soundtrack, though the performance in the movie is by someone else) - for those unfamiliar with Wainwright, his father is Loudon Wainwright III and his mother was Kate McGarrigle (The McGarrigle Sisters). He and Leonard Cohen's daughter have a child together (a little girl).
Fiona Apple - Across the Universe, The Beatles
Noel Gallagher - To Be Someone, The Jam (the original is better, but I loved this version when I saw them in Pittsburgh many moons ago...)
Radiohead - Ceremony, Joy Division/New Order (it's f'n awesome; one of my favorite JD/NO songs - it's great because they play it very, very straight and faithful to the original)
Nine Inch Nails - Dead Souls, Joy Division