Didn't read thread yet, but here's what comes to mind. Please express all agreement and disapproval.

Wild Horses - The Sundays --> One of the few covers that truly changes the sound of a song, IMO. Very close, if not better than the original.

Blue Monday - Orgy --> First version by New Order was super bland, but probably cool at the time. Definitely a good job livening this song up.

All Along the Watchtower - Hendrix --> obv choice

Layla --> Eric Clapton --> If it qualifies as a cover, this may very well be the winner

Man Who Sold the World - Nirvana --> Because Nirvana rules and truly owns this song. I don't think most people have ever even heard the original.