John James, a former record-store owner and syndicated music columnist, compiled this ginormous list, but left off some of my favorite covers:

Johnny Cash - Hurt (Nine Inch Nails)
Aretha Franklin - I Say A Little Prayer (Burt Bacharach)
Crooked Fingers - When U Were Mine (Prince)
Regina Spektor - Real Love (John Lennon)
Wilco - Love and Mercy (Brian Wilson)
Ben Lee - Float On (Modest Mouse)
Grizzly Bear - Mother and Child Reunion (Paul Simon)
eels - I’m a Loser (The Beatles)
Okkervil River - Riot Act (Elvis Costello)
Glen Hansard - Cry Me a River (Justin Timberlake)