Eva Cassidy sang some wonderful covers.
https://www.youtube.com/watch?v=bTNLYeaL7No
Singing Christine McVie's Songbird
I'm a crazy Crowded House fan and there have been dozens and dozens, probably hundreds, of covers of Tim and Neil Finn songs. Astounding song writers.
Rufus Wainwright has done some great covers including "Across the Universe"
There are some great Van Morrison and Beach Boys covers around as well.
ohhh, there are so many.