Music

You're so vain by Faster Pussycat turned out to be a cover

Cross-Eyed Mary

I also thought Man on the Silver Mountain was by Mago de OZ

Nina Hagen's version of I'm Going To Live The Life I Sing About in My Song

Nina Hagen: https://www.youtube.com/watch?v=jdiTFj0WDWc

Mahalia Jackson: https://www.youtube.com/watch?v=XXYauoAIvfA

The entire genre of Drum N Bass is a cover of the Amen break.

@DingoFan I must say I've heard the version of Hurt by Johnny Cash way before I knew it was a nine inch nails cover:

https://www.youtube.com/watch?v=8AHCfZTRGiI

(Here's the version from Nine Inch Nails):

https://www.youtube.com/watch?v=6oGqIfnIAEA

There was also an artist in my country called Lucia. She made a song called Silence which was a cover after a band called The MOOoD. I always thought her song was the original, and not the other way around:

https://www.youtube.com/watch?v=UAm_uoV1z5k

Edit: here's the original:

https://www.youtube.com/watch?v=ZYp7c9sB86c

Tennessee Ernie Ford - 16 Tons - a cover of a Merle Travis song

Apparently these are actually pretty well-known covers but I only found out a few years after:

• Tina Turner's Proud Mary is originally by Creedence Clearwater Revival
• Judas Priest's The Green Manalishi (With the Two-Pronged Crown) is a cover of a Fleetwood Mac song
• Whiskey in the Jar is apparently an Irish traditional song, so both Thin Lizzy's and Metallica's (and also the Dubliners') can be said to be covers