Hearya has a great list here of 33 cover songs better than the originals, including
All Along the Watchtower – Jimi Hendrix, 1968 (Bob Dylan)
And the Band Played Waltzing Matilda – The Pogues, 1984 (The Dubliners)
Sweet Jane – Cowboy Junkies, 1988 (Lou Reed)
Hallelujah – Jeff Buckley, 1994 (Leonard Cohen)
I Found a Reason - Cat Power, 2000 (The Velvet Underground
I'll let you decide for yourself!