Cover songs that are better than the originals.

There is an active thread about terrible cover songs so I thought I'd start one about cover songs that are better than or have completely eclipsed the originals. I'll start:

Randy Newman wrote Momma Told Me Not to Come for Eric Burdon who recored it with the Animals and Newman recorded it too. I have the Newman version and like it but Three Dog Night really seem to capture the mood of the song best in my opinion.
Thanks for correcting that slaw.
 Didn't think it sounded right.
@stvgray ,

Hey, I'm a fan of Feist. I seem to recall "Limit to Your Love". But I'm not familiar with James Blake.
Urge Overkill’s cover of Neil Diamond’s “Girl You’ll Be A Woman Soon”
Harry Nilsson’s cover of Badfinger’s “Without You”
Al Green’s cover of the Bee Gee’s “How Do You Mend A Broken Heart”
Sting’s cover of Leonard Cohen’s “Sisters Of Mercy”
Prince’s version of Joni Mitchell’s “I Could Drink A Case Of You”

The Treble With Tribbles, if you haven't heard Sister Carol's version of Wild Thing off of the "Something Wild" soundtrack, check it out.
Another excellent rendition that takes the song in a whole 'nother direction...I've put it to great use at parties in my distant dj past.

IMHO, no cover of "Sweet Jane" touchs Lou Reed's live version from Live On Letterman.....all the power, crunch, and testifying one could ask for in rock.