Godhead’s ‘Ellinoir Rigby’
As mentioned before - ‘Daytripper’ by the Bad Brains. It is a dub reggae version - very chill. Listen to a sample at http://music.channel.aol.com/album/main.adp?_pgtyp=pdct&albumid=1131
Another good one is Cornershop’s Hindi version of ‘Norweign Wood’
Check out a clip on Amazon
There’s a pianist named John Bayless who released a couple CDs of Beatles songs played (maybe even improvised) in the style of J.S. Bach.
They’re worth hearing at least once.
[sub]Someone I knew in college had a tape (origin unknown) of Beatles songs played in different classical styles, including a Hey Jude fugue. I’d like to find that one again.[/sub]
Lol Coxhill’s version of I Am the Walrus, absolutely, bar-none, the weirdest song ever recorded.
Harry Nilsson had a terrific version of You Can’t Do That, medley of about 20 other Beatles songs that lead McCartney and Lennon to name him their favorite American singer.
There’s an interesting list of Beatles covers here.
And there’s always “Sie Lieb Dich” and “Komm Gib Mir Deine Hand” by the Beatles themselvs. 
True, but the Beatles didn’t write that one. It was written by Berry Gordy Jr., and originally popularized by Barret Strong.
Jeff Beck did She’s A Woman on Blow By Blow
Deep Purple did psychedelic versions early on of Help and Bird Has Flown
Jimi did Day Tripper on Radio One (a BBC compilation)
Trivia hijack: This doesn’t surprise me, as Head’s brother is Murray Head, of “Jesus Christ Superstar” and “One Night in Bangkok” fame.
I have to find that CD.
Another vote for Bette Midler’s “In My Life.” A gorgeous, gorgeous version. (Esp. if you saw For the Boys and remember where in the movie she sang it.)
Here’s a nice obscure one: Either/Orchestra (contemporary big-band jazz) does a version of “Don’t Bother Me” on their album afro-cubism. I love sneaking that up on people, since most of my friends find my taste in music extremely eccentric and don’t expect to hear any songs they know in anything I play. 
I love Spineshank’s version of While My Guitar Gently Weeps.
Suggs’ - ‘I’m Only Sleeping’
Steve Earle’s - ‘I’m Looking Through You’
oh and Rufus’ ‘Across the Universe’ again.
The King’s Singers is an excellent British a cappella group, and their album The Beatles Connection is well worth listening to. 