Actually this might be a bit short... as I start I have four in mind (and one of them's obviously the Stones).
I was listening to this rather excellent mixcloud mix and on came this rather fab and slightly sunny cover by a band I'd never heard of called The Deep Six - it made me smile... - just after the "I see a line of cars" line there's a hilarious muppet-like 'meep meep' - AllMusic guide were not so impressed...
...even worse, "Paint It Black," which sounds as goofy as if the Serendipity Singers were performing it after taking a few tokes for the first time
Next up the ever fantastic The Feelies - the cover turned up on their first album - and they've been playing regularly during the epic sets during their recent reunion - which this weekend involves three nights at Maxwell's in Hoboken sadly too far from London!
The Mo-dettes (1980)
The Rolling Stones (1966)