Cover songs that are better than the originals.

Hard to believe that Sinead O'Conner (or anyone) topped Prince, but she did on "Nothing Compares to You." He recorded that song as if he didn't think it was anything that special, but she poured her soul into it. How about the Who's version of "Young Man Blues"? If you haven't, check out the original by Mose Allison. OMG, never heard a jazz throwaway turned into a rock masterpiece. 

+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.