House of the Rising Sun was first recorded by Leadbelly, the author is unknown and it is typically called a “traditional” tune. Lot’s of good covers. Frigid Pink had a decent one in 1970.
Mama Tried- Merle Haggard, (Grateful Dead). The Dead had a LOT of songs that weren’t original that people assumed were.
I don’t think that Linda Ronstadt ever wrote a song in her life, but just about everything she recorded was better than the original IMO.
If you’re a fan of the blue’s you probably know that a lot of British bands esp, recorded old blue’s songs in their early days. “Key to the Highway”, Derek and the Dominoes, originally recorded by Big Bill Broonzy. The Animals recorded John Lee Hookers “Boom Boom”, it hit #43 on Billboard in 1964. The Yardbirds covered “Dust my Broom” by Elmore James and in the states there are many, many examples of early blues getting covered by the emerging rock and roll generation. In America, southern rock turned to blues for their inspiration as well. My favorite was the Allman Brothers cover of “Stormy Monday”, originally written and covered by T-Bone Walker.
The Rolling Stones successfully covered more blue’s songs than any other band from this era I believe. They had a run with standards from Chess records that earned them respect not just from the fans but also from the people who had recorded the songs originally. Muddy Waters became a big fan of the Stones after they recorded a song he had made famous, “I Just Want to Make Love to You”. It also kept Chess on the map at a time that they were in risk of going under. They gave credit where credit where credit was due, unlike Led Zeppelin. Memphis Minnie wrote, “When the Levee Breaks”, but you’ll never see any credit.
I also am a big fan of Disturbed’s cover “The Sounds of Silence”, really powerful version.
One of my favorites, done as a duet, is Conway Twitty and Sam Moore’s cover of, “A Rainy Night in Georgia”.
Many great examples out there.