I like covers that are close to the original, as well as ones that are seriously improved by being different.
Different from original:
Blinded By The Light by Manfred Mann (orig Bruce Sprinsteen, yuck)
Mr Tambourine Man by The Byrds (orig Dylan)
Roll Over Beethoven by ELO (orig Chuck Berry)
I first heard the Manfred Mann's Earth band version back in '76 when I was 13 and I loved it then. It's still one of my faves and one of their greatest ever, through all the incarnations of Mann's bands. It's so beautiful and not as well timed as it seems coz alot of tape splicing took place. Actually, it's probably one of the tracks that hastened the onset of digital editing {

} in a backhand, subliminal way. I used to work with a guy that was a Springsteen obsessive and when he played Springsteen's original to me, I thought it was rubbish. But it couldn't've been that bad, Mann and his cohorts obviously saw some potential in it !
The first version of "Mr Tambourine man" I heard was the Byrds one. Absolutely love it, it's gorgeous in every way. About five years later, I heard Melanie's version. Never thought I could like another version, but hers is superlative and pushes the Byrds veeeeery close. Then some 11 years after first hearing the Byrds version, I heard the original by Dylan. Sheeeeeesh kebab ! What a knockout ! It's the best of the three. It's one of the few songs I can think of that has three versions that I'd happilly take to a desert island.
As a complete surprize, I like both Chuck Berry and the Beatles' versions of "Roll over Beethoven". But there's a version that drives both into the ground, and then some ! It's by a group I've long referred to as 'The Fakes'. Over here in England, in the 70s there were tons of these crummy compilation albums of popular songs but not by the original artists, not even cover versions by 'name' artists. These were put together by faceless unknown session musicians and singers and put out cheaply. There was this "50 great rock'n'roll hits" and I do like the versions on it; they are, I guess, an insult to the originals but I think some of them are great. I don't know whose version "Roll over Beethoven" is based on but it ain't Berry's or the Beatles' and it's so over the top and bombastic. It's fantastic.