Not a studio version, but with the band backing him up, I'll put it up against nearly any studio recording!
Stevie Wonder - We Can Work It Out
Funky 70's Stevie covering the Beatles, how can you not love it?
Earth, Wind, & Fire - Got to Get You Into My Life
Another R&B Beatles cover with a totally original take, and one of the only redeeming things to come out of the Sgt. Peppers movie.
Aretha Franklin - Eleanor Rigby
That'll complete my triumvurate of funky Beatles covers... though I'm tempted to include Marvin Gaye's Yesterday, it's just as good.
Rolling Stones - Not Fade Away
The Stones re-Diddleyized what Buddy Holly countrified, and it probably sounds better than the Holly original and the Diddley records that inspired it.
This was a revelation the first time I heard it, don't know what else to say.
Just the drums alone make this one worth a listen.
Tuts & The Maytals - Louie Louie
Reggae pioneers reinvent a rock classic, and you might actually be able to hear the lyrics, if you can get past the Jamaican accent!
Seger System - River Deep, Mountain High
Another live one, but with Seger, that's a bonus. Not much room for improvement over Tina's version, but this one doesn't disappoint.
Rush did an album awhile back just of covers, its called “Feedback”. Songs that they loved and influenced them as they were growing up.
“Summertime Blues” is real good on it, but my favorite is probably “Crossroads” made famous by Eric Clapton:
http://www.youtube.com/watch?v=-9B3VWu_BZ8