Having mentioned below the cover of a Smiths song, I thought I would list my favourite cover versions.
The Man Who Sold the Earth - Nirvana
Lost in Music - The Fall
Come Together - Ike & Tina Turner
Winterlong - The Pixies
Brass in Pocket - Suede
Hallelujah - Jeff Buckley
Jump into the Fire - LCD Soundsystem
Sympathy - Janes Addiction
Hounds of Love - The Futureheads
Ms Jackson - The Vines
All Along the Watch Tower - Jimi Hendrix
Girl, You'll Be a Woman Soon - Urge Overkill
Dolphins - Beth Orton and Terry Callier
and then the multiple entries from Johnny Cash (the king of cover versions):
and our course, Primal Scream's covers of Kick Out the Jams, Born to Lose and Slip Inside This House.
I would also probably also add Candy Flip's version of Strawberry Fields Forever, which I realise is pretty dreadful but it reminds me of my formative years...