I have a few that come to mind:
David Bowie's cover of the Beach Boys' "God Only Knows" is awesome, his vocal range finally does the song justice. Pick up a copy of Bowie's "Tonight" album and see if you agree.
For some odd reason I really dig the Fine Young Cannibal's cover of Elvis' "Suspicious Minds". Upbeat, rockin', just plainly fun.
Tom Cochrane does a terrific job of covering Leonard Cohen's "Bird on a Wire". The addition of some very tasteful acoustic guitar and a more melodic vocal approach really makes the song shine!
I like Metallica's version of Bob Seger's "Turn the Page". Harder edge while maintaining the essence of the tune.