wow... I have no idea why I never saw this thread before...the two that immediately come to mind are:
bob dylan's all along the watchtower/jimi hendrix
the kinks' you really got me/van halen
I think those 2 songs are widely regarded (at least among us older folk) as two of the greatest covers of all time. so good that they made the songs their own. in hendrix's case, he totally reworked the tune. all VH did really was speed the song up.... but both have so much more fire and energy than the originals that I'd rather hear the covers any day. hell, after VH broke, when the kinks played you really got me it sounded like they were trying to copy VH's version, except dave davies is a far cry from eddie van halen.