Cover tunes better than the originals?

[HoopHog]

What cover tunes (remakes) do you think are better than the original tune?

Here are a few personal selections:

Close Up The Honky Tonks
- Dwight Yoakum's instead of Buck Owens
Here, There and Everywhere
- EmmyLou Harris instead of The Beatles
Hurt
- Johnny Cash instead of Nine Inch Nails
Sweet Jane
- Cowboy Junkies instead of Lou Reed
High and Dry
- Jamie Cullum instead of Radiohead

I could have listed many of the British bands who sufficiently covered many of the American blues standards, but there are too many great examples to mention.

What are some of your selections?