I've mentioned this one before, but
The Puppini Sisters - Wuthering Heights
Their version is quite funny, but what's funnier is the extent to which it seems to offend the die-hard Kate Bush fans who have no sense of humour.

The Byrds - Mr Tambourine Man
Easier on the ears than the original

The Who - Shakin' All Over
Nothing wrong with Johnny Kidd's original, it just doesn't quite cut the mustard after you've heard the version from The Who Live at Leeds.

EDIT: How did I forget?
Johnny Winter - Highway 61 Revisited
Look it up. You know it's the way Bob Dylan would have wanted it.

EDIT EDIT:
Mike Flowers - Wonderwall
This one depends on your own personal balance between sense of humour and hatred of Oasis.
(LongJohnBaldry, Wed 12 May 2010, 11:06, 3 replies, latest was 16 years ago)

I'm not sure I 100% agree on the last one
but Live at Leeds is one of the best records of all time, for sure.
( Monty Boyce, My cheese game is strong, Wed 12 May 2010, 11:10, Reply)

I think it's about the chronological order of their discovery by me
I didn't hear the Pirates' version until a couple of years after The Who. The original is wonderfully atmospheric, but I think The Who's version is more likely to make you shake all over - they're surprisingly different given that all The Who did, ostensibly, was play it louder and a bit more in their own idiom.
(LongJohnBaldry, Wed 12 May 2010, 11:24, Reply)

I've heard that Puppini Sisters version
I like it, but I can't quite equate it with the original, it's so different.

Dommin - I Just Died in Your Arms Tonight

Nightwish - Over the hills and far away. Much more epic than the original.

Apocalyptica - A lot of the Metallica stuff they cover.
(Applebite Uh! A cow!, Wed 12 May 2010, 11:10, Reply)

the apocalyptica stuff isn't better than the originals though
I will have to check out that Nightwish cover. Sounds like it will be awesome.
( Vipros. clever got me this far, then tricky got me in, Wed 12 May 2010, 11:11, Reply)

I love the solo in the middle. Fantastic.
It's the Gary Moore song they covered, not the Led Zeppelin one by the way.

A couple of them are.
(Applebite Uh! A cow!, Wed 12 May 2010, 11:16, Reply)

ah ok
still good though.
( Vipros. clever got me this far, then tricky got me in, Wed 12 May 2010, 11:18, Reply)

Johnny Winter's cover
of Gangster of Love by Johny Guitar Watson is one of my all time favourite tunes.
( Monty Boyce, My cheese game is strong, Wed 12 May 2010, 11:15, Reply)

I've not heard that one
Any idea which album it's from?
(LongJohnBaldry, Wed 12 May 2010, 11:20, Reply)

It was a single.
You can get it on one of those 'early years' type compilations.
( Monty Boyce, My cheese game is strong, Wed 12 May 2010, 11:22, Reply)