Some say Nilsson’s version of* “Without You”* is better than Badfinger’s original version. Mariah Carey’s version is best unheard.
I like The English Beat’s ska version of Smokey Robinson’s, ‘The Tears of a Clown’.
(Note: I added the link.) Thank you for mentioning this one - I love that version!
For the uninitiated, the Beatnix do “Stairway” in the style of the 1964 Beatles.
I like the English Beat, but I must disagree.
Well, going back even further…Peter, Paul & Mary’s cover was what made John Denver famous.
But John Denver’s cover of Darcy Farrow was better than the original.
Nah, the original is easily better.
The Headstones could be singing pretty much any lyrics, and you wouldn’t know the difference. Especially on the refrain.
I remember looking at the PP&M album back in 1969 or 1970 and thinking, “who is ‘Deutschendorf’?” 
ETA: Damn, I had no idea he’d died all the way back in 1997. Guess I’ll leave him off my Death Pool list!
Also Wall of Voodoo’s cover. I like all three.
I will nominate Yes’s version of both the Beatles Every Little Thing and Paul Simon’s America.
And of course The Dickies version of Eve of Destruction and Knights in White Satin.
^^^love these guys! - “…cause my momma ain’t ho-home…”
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Better than the original? Hard to say, the original’s a tough act to follow: