I guess some of my favorites are among the aforementioned "obvious" choices, including Hendrix's cover of Dylan's "All Along the Watchtower", Joe Cocker's "With A Little Help From My Friends", and Jeff Buckley's "Hallelujah". Johnny Cash's "Hurt" always gives me goosebumps!
The most haunting, to me, are Sinead O'Conner's cover of Prince's "Nothing Compares 2U"
and Gary Jules' cover of Tears for Fears' "Mad World" (which I first saw in a video game commercial, of all places!)
Then there's a perennial favorite Joan Jett and the Blackhearts' cover of The Arrows' "I Love Rock and Roll"
Which was then covered by Brittney Spears (badly? You decide)
Worst? No question from my point of view...