Though it's already been mentioned: Gary Jules - Mad World http://www.youtube.com/watch?v=4N3N1MlvVc4
Panic at the Disco - Northern Downpour http://www.youtube.com/watch?v=zouSojyIi94&ob=av3e
Johnny Cash - Hurt http://www.youtube.com/watch?v=o22eIJDtKho
Leonard Cohen - Hallelujah http://www.youtube.com/watch?v=YrLk4vdY28Q
I may not agree with the second (not in the least) the fact that you posted Leonard Cohen makes up for that. I love Leonard Cohen Songs of Love and Hate is my preferred album, [censored] musical genius man.
http://www.youtube.com/watch?v=OW3_j6SoHXM
I highly recommend anybody with even a remote interest in folk music to listen to this timeless album.
I'll post a few more
Tim Buckley (no, not the bad webcomics guy) http://www.youtube.com/watch?v=vMTEtDBHGY4 Genre: Folk
Planning for Burial http://www.youtube.com/watch?v=CcdmYpF55l0 Genre: Sludge, shoegaze or something, don't know, check it out
Deerhunter http://www.youtube.com/watch?v=32dLVXMzgTg Genre: Listed as shoegaze