So anyone care to weigh in with other Beatles songs that they feel were done better by others? I am a fan, and can’t think of any for me right off, but maybe…
Next question then: Elton John’s “Rocket Man” or William Shatner’s “Rocket Man”?
I’ve got a slight preference for the Rufus Wainwright version of “Across the Universe.”
Joe Cockers “Darling be home soon” or Sebastian Cabots “Mr Tambourine Man”
Fiona Apple – “Across the Universe”
Pat Benatar - “Helter Skelter”
The Breeders – “Happiness Is a Warm Gun”
Calamity Jane - “I’ve Just Seen a Face”
Johnny Cash- “In My Life”
Fats Domino - “Lady Madonna”
Echo and the Bunnymen – “Ticket to Ride”
Al Green – “I Want to Hold Your Hand”
Jimi Hendrix - “Sgt Pepper’s Lonely Hearts Club Band”
Alison Krauss – “I Will”
Willie Nelson - “Yesterday”
Elliott Smith – “Because”
Peter Tosh - “Here Comes The Sun”
Link Wray - “Please Please Me”
Your taste determines the answer. If you love Sinatra, you’ll prefer his version of Something; Ray Charles fans like his version of Eleanor Rigby. Richie Havens version of* Here Comes the Sun* got a big boost because of Woodstock.
Personally, I’ve always been fond of Judy Collins’In My Life.
Johnny Paycheck did a pretty nice version of “Something”.
Covers are a compliment for songwriters and artists. It says a lot that so many great artists want to record Lennon-McCartney songs.
Here is their catalog. Quite a body of work.
I like some of the covers. Fats Domino - “Lady Madonna” Bon Jovi Here Comes the Sun
But the originals by the Beatles are my favorites. The one exception is Cocker’s Little Help From My Friends. Jimmy Page on lead guitar, and Joe’s vocals. Great combination.
Roll Over Beethoven 
I like the Richie Havens one mentioned. I don’t know most of the others. However I heard a Muzak version of Goodnight which was not significantly worse than the one on the White Album.
It’s hard to believe you’re a Beatles fan if you’re saying all those are better than the originals. Elliot Smiths is a carbon recreation. Johnny Cashs and Al Greens are a completely whole other ball of wax. i think that johnny did it on suggestion of the record producer, not that he isn’t great and got his own ideas.
I haven’t heard one yet. It’s not so easy to best an original. Look, how many people did a Chuck Berry song better than Chuck? To me only one: The Rolling Stones Route 66 (Chucks version). The Beatles never came close.
Rock and Roll is overwrought, dude. The Beatles were usually not rockers, especially not by that point.
I see later Lennon and McCartney like I see Dylan, as songwriters who made a few bucks on the side with what sometimes seem like demo albums. Songwriting is where the royalties lie.
I would disagree. I think making their albums was where the Beatles put the primary focus of their attention. There are performers who take a haphazard approach to recording; but by all accounts the Beatles were the opposite. They were very deeply concerned and involved with minute details of the process.
Paul was very concerned. 
I’m not sure the others shared his [DEL]obsession[/DEL] passion for studio work. Didn’t the endless days in the studio contribute to their breakup?
Cocker’s whining, tortured, raspy voice is the pits. The Beatle’s version is totally perfect.
You know Joe’s widow is a member here, right?
Joe Cocker all the way!~
Somewhat recently I saw an interview with someone – I forget who it was – and they were talking about how Beatles were essentially studio musicians because they couldn’t play live. Not that they were incapable, of course, but every time they tried they were drowned out by the incessant cacophony of teenage girls screaming bloody murder. So they never really honed any stagecraft. (They have what, one live album, which is almost impossible to get because it sucks?)
I believe it was in this same interview they talk about how the Joe Cocker version was played for Paul, who responded very positively to it.
It could conceivably have been an interview with Paul himself, but I can’t remember who it was. Or I could have dreamed the whole thing for all I can remember.
I personally voted Joe Cocker, and it wasn’t even close. But I’m a jam-band kind of guy, having gone to countless Grateful Dead (until Jerry died) and Phish shows. Joe’s version is right in my wheelhouse, and the video of him doing the song at Woodstock is practically my nirvana. (The paradise, not the band.)
Actually, the note about Paul liking Cocker’s version was from press when Cocker died. Here’s an article with the quote I was thinking of:
I’ll say one thing: maybe it’s because I heard it first, but “do” sounds so much better to me in that first line than “think”.
But I wasn’t talking about her, and I doubt you’re being serious.