Superchunk's cover of "100,000 Fireflies" is pretty darn good. As is The Wedding Present's cover of "It's Not Unusual."
I actually like the Beatles cover of[Please Mr Postman-The Marvelettes]...the Moments cover of[If I Didn't Care-The Inkspots]...The Four Tops cover of[Michelle-The Beatles]...Chubby Checker's cover of[The Twist-Hank Ballard].
Ramblin' Jack Elliott - Pony Tom Waits recorded this song on his 1999 album "Mule Variations". The great Ramblin' Jack Eliott did a cover on his album "The Last Ride" (HighTone, 2006). It's in a faster tempo than Tom Waits' original, but nearly as rugged and jagged. Joe Craven's banjo adds a nice old-time vibe to the tune. "And I hope my pony I hope my pony I hope my pony Knows the way back home"
Black Joe Lewis , Since I met You Baby, when i first heard this I thought what the ? but it quickly became one of my favorite songs. Check out the horns at 1:35. Since I Met You Baby" written and recorded by pianist Ivory Joe Hunter in 1956
The Gun Club - Cool Drink of Water Blues The original was recorded in Memphis/Tennessee by Tommy Johnson in 1928. Released on Victor Records the same year. The Gun Club covered the song on their debut album "Fire of Love" in 1981. Jeffrey Lee Pierce's rambling swamp vocals and feverish, possessed and hell-bound performance just make this iconic blues standard sound like it would be his own song.
I am a big fan of the album "red on Blonde' by Tim O'Brien. An entire album of Dylan covers without a clunker in the lot IMO. Any Dylan fan should seek it out.
Take Me to the River - Al Green. As much as I dig Al's vocal - I really prefer the laid back Talking Heads cover.