Cover songs that are better than the originals.

+1 on Hendrix All Along the Watchtower 
Hendrix - Gloria 
Minor Threat's version of Stepping Stone 
Iron & Wine - Such Great Heights from the Postal Service 
Lynyrd Skynyrd- Call Me The Breeze 
Willie Nelson- Wisky River (and about 20 other songs)
Cake - I Will Survive 
Pretenders - Thin Line Between Love and Hate 
+1 Talking Heads - Take Me to the River
Dandy Warhols - Hells Bells
Devo - Satisfaction 
Plenty of others 

Allison Moore's recording of "Both Sides Now" (on her Mockingbird album), which I prefer to those by both Joni and Judy. 

Yes mic ,I have it and talk about Simon n Garfunkle .Thats a close race between them and Bob Dylan over who'a songs have been covered more .I guess the Beatles go in the mix .But as a single songwriter  I would think ,Bob Dylan wins.

Lots of good stuff here. But it seems like we're getting into some esoteric stuff in regard to some covering musicians.

Obviously music is a matter of taste and it is going to be common for someone to hear a cover by a band or artist and like the cover better than the original but other than that there isn't much to support the cover being better than the original. My example of Jerry Lee Lewis doing "Over the Rainbow". That pretty much just comes down to me since not many people have ever heard Lewis's cover of that song including Wikipedia.

So maybe we should narrow the field and rather than saying covers that are better than the original or that eclipsed the original, maybe we should say covers that are better than AND have eclipsed the original in terms of critical reception, sales, popularity etc.

I think the "AND" is important because there are notable covers that eclipsed the original but are still pretty awful..."The Night They Drove Old Dixie Down" by Joan Baez being a prime example. She made it a hit song but she also made it an awful song.