Jeff Buckley's Lilac Wine and Hallelujah for starters. Allison Crowe's cover of Joni Mitchell's River and Leonard Cohen's Hallelujah are both really good as well.
Another personal favorite of mine is the Joan Baez cover of Forever Young.
And as noted before The Clash's I fought the Law and Nirvana's The Man Who Sold the World are both really, really good as well.
Ghost of Tom Joad is by Bruce Springsteen. Rage Against the Machine covered it. It's an excellent song ion both instances though. Although the cover is inferior in my opinion.
I would like to add Hurt, after hearing it for the first time a few days ago. Of course it was already mentioned..I just like to portray my ignorance.
Along the Watchtower by Jimi Hendrix (Bob Dylan original)
Turn the Page by Metallica (Bob Siegert original)
Over The Hills And Far Away by Jimi Hendrix and Nightwish (Led Zepplin original)
Fire by Magni Asgeirsson (Jimi Hendrix original) - don't shoot me for liking it just because on Rockstar Supernova as it was actually awesome