I can’t stop listeing to Brad Mehldau’s version of She’s Leaving Home.
And, though it’s George Harrison solo, and not the Beatles, another favorite is Nina Simone’s version of Isn’t It A Pity.
/nitpick - I love the Flying Lizard cover but The Beatles version is a cover of Barret Strong’s 1959 original hit.
U2’s cover of Helter Skelteris OK, but I really love Motley Crue’s version, it just has a great post-punk metal sound.
We Can Work It Out by Stevie Wonder.
“Every Little Thing” by Yes. And “I’m Looking Through You” by Steve Earle.
And I Love Her done by a very young pre-reggae superstar Bob Marley. The horns handling George Harrison’s awesome hook just slay me.
Elliot Smith doing Because. One of my all time favorite musical acts covering one my all time favorite musical acts.
“And Your Bird Can Sing” by Guadalcanal Diary
Baby It’s You was covered by the Beatles, but Smith covered it better-
James Taylor - Day Tripper
Art Garfunkel - I Will
Emmylou Harris - For No One
One Direction - All You Need Is Love 
Rufus, Moby, & Sean Lennon - Across The Universe
The Carpenters - Ticket To Ride
In My Life - Judy Collins
Chikezie - She’s A Woman
Spookey Tooth - I Am The Walrus
Lil Wayne - Help
I’m not sure if that’s wonderful or horrible, but it is amazing.
This*, on the other hand, is sublime: terrible in every way, yet transfixing in its awfulness.
*William Shatner’s Lucy in the Sky with Diamonds
Working Class Hero Marianne Faithfull
I think this is the definitive version, myself.
Not a Beatles song, unless you stretch the definition to include songs by ex-Beatles.
As I pointed out back in post 26.
well, okay. Still one of my favorite covers.
Cheap Trick used to do a fine live version of* Day Tripper*. I’m surprised no one’s mentioned it yet.
Ah, almost forgot: Vanilla Fudge’s Ticket To Ride.
Greatest cover ever:
Joe Cocker, With a Little Help from my Friends
They did a pretty decent version of the whole of Sgt. Pepper too. I like Robyn Hitchcock’s versionbetter though, mostly because of the between-song banter.
Hells yeah. That song BELONGS to Stevie in this version.