re: Covers That You Like Better Than the Original

Don't know if any of these have been mentioned:

Suzie Q by CCR (Dale Hawkins)
Whole Lotta Shakin' Going On by Jerry Lee Lewis (Big Maybelle)
Mr. Tamborine Man by The Byrds (Bob Dylan)
Statesboro Blues by Allman Brothers
Respect by Aretha Franklin
Twist and Shout by The Beatles
Black Magic Woman by Santana
Blue Suede Shoes by Elvis Presley
Wild Thing by the Troggs
Blueberry Hill by Fats Domino (Gene Autry)

Here's a bonus: Ring of Fire by Johnny Cash (It was first recorded by Anita Carter, Cash's sister-in-law.)

Speaking of,

Streets of Bakersfield