If you cover a song, and you're not an above-the-rules god like Johnny Cash, you can generally do one of three things with it -- that's if you want to cover it well and not just do a completely faithful re-recording: You can "pump it up," injecting extra power into it, along the lines of, say, Disturbed's version of Land of Confusion or the Bangles' spectacular cover of Hazy Shade of Winter; you can acousticize it, as Buckley did with his staggeringly beautiful version of Hallelujah; or you can completely reimagine it.
This last choice is a lot trickier and more dangerous, but when it pays off, the dividends are huge. Just look at Placebo's take on Kate Bush's Running Up That Hill, any of the covers ever done by the bands Greg Dulli has played in throughout the years -- or this, one of my all-time favorite covers, by Matchbox 20.
To truly appreciate the just how clever this song is, you have to listen to the original source material, from Fleetwood Mac's Rumours album. These guys took the most throwaway track on that album, a folksy little ditty, then actually combined it stylistically with a second song from the same album -- the gorgeously dark and menacing The Chain -- and the result is something very, very cool.
Here's Matchbox 20 doing Never Going Back Again.