I definitely agree about Placebo's "Running Up That Hill." I've heard a few other versions but that's my favourite. I also love Tori Amos doing The Cure's "Lovesong", but I like the original too. Speaking of "Lovesong", there's a really interesting version of that one done by A Perfect Circle; it's combined with Ozzy Osbourne's "Diary of A Madman". Very cool.
I am usually in favour of covers, and don't really understand the absolute distress some people feel about them; the original still exists, after all. Then again I also love things like redone fairy tales. I dislike covers that seem to 'blandify' them; I don't mind a different stye, but making it into elevator music seems rather pointless.