To add to the Hendrix blasphemy mentioned above, I prefer Walter Trout's version of Red House. 

We could probably have an entire thread about who's version of Autumn Leaves is best!  LOL!  
 

Soft Cell's "Tainted Love." The original was great, but Marc Almond's gritty 80's synth pop version did the song more justice in my opinion, even if the video was kinda creepy. 

Also Tool's cover of "No Quarter" is thoroughly awesome
 

Sharke just reminded me of this remake:
 

Oops!  I put the wrong video in my last reply...  Oh well, that's a good song too!  Here's what I intended:
 

I hated early 80's synth pop at the time but I love it now. For some reason. 

IMO it's so easy to revamp a song to fit the taste of the day or the style of a "hot today"-artist, that I don't want to call the remakes any better than the originals. The fact that a remake version sounds more fresh or something is often obvious, especially talking about arrangements. Also, the original can be made rather cheaply By beginners and the cover is an expensive high end production By the hottest names in the industry.
 
Of course, you can't deny the fact that some singers and instrumentalists are better or sound better for the song in question than some other.
Rod Stewarts version of "Sailing" is an easy example, and Hanoi Rocks'  version of "Up around the bend" is a good example of simple production vs. big production and the taste of the day.

I've heard some terrible covers on the radio over the last few years, but I've never bothered to find out who they were. Usually it's some classic 60's or 70's song being sterilized by some generic shrink-wrapped vocalist who sings in that bland "American Idol" style. I think one of them was Joni Mitchell's "Big Yellow Taxi." The instrumentation on these things is usually intensely forgettable as well. 

craigb
Oops!  I put the wrong video in my last reply...  Oh well, that's a good song too!  Here's what I intended:
 

Yikes. No auto-tune back then