Cover songs that are better than the originals.

There is an active thread about terrible cover songs so I thought I'd start one about cover songs that are better than or have completely eclipsed the originals. I'll start:

Randy Newman wrote Momma Told Me Not to Come for Eric Burdon who recored it with the Animals and Newman recorded it too. I have the Newman version and like it but Three Dog Night really seem to capture the mood of the song best in my opinion.
Lloyd Cole: "Chelsea Hotel"
Poco: "Magnolia"
Rosanne Cash: "River"
Translator: "Today"
Bryan Ferry: "All Tomorrow's Parties"
Mott the Hoople: "Sweet Jane"
The Primitives: "I'll Be Your Mirror"
Allison Krause: "Can't Find My Way Home"
Jeffrey Gaines: "Win"
Three Dog Night: "Eli's Coming"
Linda Ronstadt: "Party Girl"
The Jam: "David Watts"
Buffalo Tom: "Going Underground"
Led Zeppelin — “Dazed and Confused” (Jake Holmes)
The Fugees — “Killing Me Softly With His Song” (Charles Fox/Norman Gimbel/Lori Lieberman)
Patti Smith — “Because the Night (Bruce Springsteen)
Nirvana — “The Man Who Sold the World” (David Bowie)

Ryan Adams' version of Taylor Swift's album 1989. Was it a goof?  Was it an actual tribute? I don't know. I've never heard the TS versions of these songs (except "Shake It Off") ---but I can't imagine I'd like them as much as I like this album by Ryan Adams.