The Sundays - Wild Horses (I forgot who the original is..)
The Rolling Stones! The 6ths (Or was it the Mag Fields? Or one of Mr. Merrit's other bands?) did a cover of Don't You Want Me? that I adore. Just in addition to you mentioning them.
Micah P. Hinson-Pale Blue Eyes (Velvet Underground)
Pixies-Head On (Jesus and Mary Chain)
Calexico-Alone Again, Or (Love)
The Decemberists-Bridges and Balloons (Joanna Newsom)
Sleater KInney-More Thana Feeling (I forget.)
The Bees-A Minha Menina (Os Mutantes)
OF COURSE Jimi Hendrix-All Along the Watchtower (Bob Dylan)
William Shatner-Common People (Blur)
The Byrds-Mr. Tambourine Man (Bob Dylan)
Frank Sinatra-Mrs. Robinson (Simon and Garfunkel)
Styx-I Am the Walrus
The Wailers(and everyone ever)-Louie Louie (Richard Berry... NOT THE KINGSMEN!)
Lou Barlow-Round n round (RATT)
yeah!
I am not saying that these covers are better than the original, I am just saying that I think they are pretty awesome.