Cover songs that are better than the originals.

There is an active thread about terrible cover songs so I thought I'd start one about cover songs that are better than or have completely eclipsed the originals. I'll start:

Randy Newman wrote Momma Told Me Not to Come for Eric Burdon who recored it with the Animals and Newman recorded it too. I have the Newman version and like it but Three Dog Night really seem to capture the mood of the song best in my opinion.
I have to say, I do not care for the Joe Cocker version of "A Little Help from My Friends.

I also prefer the CCR version of Proud Mary. I like watching Tina perform it but still think the CCR version is a lot better.

I suspect I'm the odd man out on these two.
SRV - Texas Flood
Joe Cocker - Unchain My Heart
Joe Cocker - You Can Leave Your Hat On

"Mystery Train" has been covered by many, Elvis, being the most famous. Here's a couple more that are definitely better than the original,

Junior Wells
Brian Setzer

And how could we overlook, "That's All Right" by Elvis or

For Proud Mary, Ike and Tina Turner vs. CCR, I think Ike Turner's vocal sets the song up so well for Tina Turner.

I like watching Ike and Tina Turner doing Proud Mary but I prefer listening to CCR.