Not that I've tried to search out bad ones. I'm sure they exist.

But I think the plethora of good covers show how (often deceptively) strong his songs are.

Unfortunately can't find the video of John Legend on Fallon, but here's another live rendition of his for Dancing in the Dark. But the Roots version is incredible:

http://www.youtube.com/watch?v=Jtn_OV1ZCAw

Basia Bulat - Glory Days. Man this is some cool instrumentation.
http://www.avclub.com/articles/basia-bulat-covers-bruce-springsteen,97089/

Johnny Cash - I'm on Fire
http://www.youtube.com/watch?v=kHLQPgrSfWY

Casiotone for the Painfully Alone - Philadelphia.
http://www.youtube.com/watch?v=hL7W1nluzUU

Aidan Moffat- Another stripped down version.
http://www.myspace.com/fuckinaidanjohnmoffat/music/songs/hungry-heart-37694577
(best link I could find)

Dar Williams: Highway Patrolman. Sentimental favorite. Years ago, my girlfriend played this and it made me reevaluate my position on Springsteen. One of my favorite stories in song ever.
http://www.youtube.com/watch?v=7VhvOX3SPoU

I know these skew lofi indie. Post your favorites.