Cover songs that are better than the originals.

Better is a very loaded term.  I'm not saying they are better, but...
Rolling Stones' "Satisfaction" by Otis ReddingBob Dylan's "Blind Willie McTell" by Mick TaylorPaul Simon's "American Tune" by Willie NelsonWailer's "Get Up, Stand Up" by Ojos de BrujoTraffic's "No Time To Live" by Johnny Winter AndAl Green's "Love And Happiness" by Toots HibbertEarl King's "Come On" by Jimi HendrixDionne Warwick's "I Say A Little Prayer" by Aretha Franklin

Birdy's cover of The National's "Skinny Love" The first time I heard it (on vinyl), I had tears welling up in my eyes. Did you hear that @n80? ??

Much as I love The Byrds, it almost pains me to say Tom Petty and The Heartbreakers did a much better job with “Feel A Whole Lot Better (When You’re Gone)”. 

Nirvana doing Bowie’s “Man Who Sold The World”

Led Zeppelin did many great covers.

Dazed and Confused
Since I have been loving you

etc.

Probably the greatest cover band ever. They improved upon and improvised upon stuff. Jimmy Page and Plant were great at seeing potential in stuff and making it 10x better

Who has ever heard of Jake Holmes or Moby Grape? I rest my case.