Harry Nilsson was a great songwriter but his biggest hits, “Without You” and “Everybody’s Talking”, were written by other people.
Nits to pick: “Nothing Compares 2 U.”
I’ve had this song going through my head for three days now, for no apparent reason. Maybe it just wanted to be mentioned in this thread:
Judy Collins, singing “Both Sides Now”, written by Joni Mitchell
(Although it’s been the Mitchell version going through my head, my husband insisted it was Judy Collins’ version that “normal people” remember best, and that it’s her best known song. 
)
Thanks, I fixed it right as you were typing that. Damn Internets.
Janis Joplin singing “Bobby McGee”
I used to her that a lot when I was a little kid, and I really liked the song. I actually developed in my head of what Bobby looked like. Then I heard Mac Davis sing it. Man, was that disturbing to a 7-year-old.
They also did “For You” and “Spirit in the Night”, Springsteen songs.
Also, Garth Brooks writes his own songs but considers his best hit “The Dance” and it was written by a colleague of his.
The OP’s linked thread brings up a good point about songs like this (and Manfred Mann’s “Blinded by the Light.”). Jimi or the Manfred band at the time may not have written the lyrics or the basic chord structure, but there’s no question that Bob Dylan would never have taken “Watchtower” as far over the edge of utter asskicking as Jimi’s version did. I’d argue that Hendrix as much wrote that song as Dylan did, taking it from a three chord acoustic strummer to a scorching electric rock classic that every kid in a garage band dreams to play half so well.
I’ve seen an interview with Kris Kristofferson where he said that even though he wrote “Me and Bobby McGee” and first performed it, he’s honored to take a backseat and call Janis’ version the original.
Maybe this is a topic for a new thread, but I can’t picture many of these songs as an artist’s “signature” song. If I had to pick I’d say these bands wrote their signature song…
Cake: "I Will Survive"
“The Distance” was their biggest hit and still plays on radio. “I Will Survive” really doesn’t.
Rolling Stones: "It’s All Over Now"
I’ve never even heard of this one and I would say the Rolling Stones are known for stuff like “Paint It Black”, “Symphony For the Devil”, “Time Is On My Side”, etc.
Pearl Jam: "Last Kiss"
What about “Jeremy”? Watching that video is like seeing Eddie Vedder’s audition for the Walkin’ Dude.
The Beatles: "Twist & Shout"
“Hey Jude”? “Yesterday”? Dozens of other songs?
Bruce Springsteen: "Jersey Girl"
What about “Born in the USA”?
You have a point Justin_Bailey–If you ask most people for a Springsteen song, you’d probably get “Born in the USA” or “Born to Run.” But if you ask "Who sings “Jersey Girl’” most everybody on the planet (or at least ouside New Jersey) will say “Springsteen.”
I was going to say Jim Croce and “I Got A Name”. Because back when I was in school, I remember a friend of mine, who was a Croce fan, telling me that this was one of the only songs Croce sang that he didn’t write. And I always believed this.
But before posting this fact, I wanted to look up who the actual songwriter was. And as far as I can tell via a quick online search, Croce did write the song.
All of these years, I’ve been living a lie.
They Might Be Giants write the vast majority of their stuff, but one of their biggest hits, “Istanbul (Not Constantinople)”, was a cover.
Croce’s own site acknowledges the writers as Charles Fox and Norman Gimbel. Your friend is right.
…though I will say I understand the confusion, because it sounds so much like a Jim Croce song.
My faith is restored.
Speaking of Springsteen, he wrote the Pointer Sisters’ huge hit “Fire”. And Patti Smith’s “Because the Night”.
Jeremy is their signature song and the one that made them famous. Last Kiss is their biggest hit, though.
Actually we’re both wrong. “Daughter” and “Better Man” both charted higher.
Did Manfred Mann write anything at all?
Did Bernie Taupin perform any of his songs?
He was primarily known for cover songs, though Paul Jones and Mike Hugg of the group wrote a few. It doesn’t look like Manfred Mann himself wrote much of anything.
IIRC, he did do a few albums, but recited the lyrics as poems instead of singing them. Bernie evidently didn’t have much of a voice.
I don’t know if Mott the Hoople wrote any of their songs, but Ian Hunter (who was in the band) did. Still, “All the Young Dudes” (written by David Bowie) seems to be the only thing they’re known for.
Joe Cocker did write a few of his own songs, but I don’t think anyone listens to them.
Someone who has my anti-taste in music told me that UB40 wrote some songs - but I don’t think they ever had a hit with any of them.
If you were too young for the 70’s, Cheap Trick is known for only one song - “The Flame”, which they didn’t write.