A lot of stuff I would have posted has already been so, so I'll throw these out there:
Eric Clapton's cover of Bob Marley's "I Shot the Sheriff"
http://www.youtube.com/watch?v=tRgcwT9X2J8
Also, some of the stuff posted by Jennifer Warnes as covers of Leonard Cohen's work are actually the other way 'round: Cohen wrote them but Warnes recorded them first. Examples include "
Ain't No Cure For Love" and "
First We Take Manhattan".