“Istanbul (Not Constantinople)” is not a They Might Be Giants original; it was first a hit in 1954.
When I was a kid in the 1970s, we thought the “Shaving Cream” song was hilarious and didn’t understand why our parents were unhappy about us singing it. Yeah, they had heard it before, and got it.
I had that album and loved his version of the song. When Juice Newton’s version came out, it just seemed a little limp.
My second favorite song on the album was Crawling from the Wreckage. I used to love singing along at the top of my lungs.
Dr. Demento?
We saw a local reggae band that we really like last night at a brewery. They do a cover of the song Superstar made famous by The Carpenters. (Long ago, and, oh, so far away I fell in love with you before the second show)
They do a brilliant cover. Soulful, reggaefied just a bit. Really beautiful.
A woman near us told me that the lead singer wrote the song. I had to find it online to show her it was written by Bonnie Lynn Bramlett , Delaney Bramlett, and Leon Russell. She was astounded. (She was in her twenties)
And if I remember correctly, Crawling from the Wreckage was a cover of a Graham Parker song.
My sister’s ex-husband, a lifelong music and RHCP fan, talked really disparagingly about the “elevator music of Stevie Wonder, creator of the terrible I Just Called To Say I Love You”.
I had to educate him, and put Innervisions, side two on the platter. With Higher Ground blasting out, he was left dumbfounded and educated.
I didn’t see it upthread so if it was already mentioned, sorry.
Bruce wrote and recorded Blinded by the Light for 1973’s Greetings from Asbury Park, NJ. Manfred Mann’s Earth Band covered it and it reached #1 in the U.S. in 1977. This version was Springsteen’s only #1 song as song writer. (Dancing in the Dark made it to #2)
Frank Sinatra’s “My Way” is a remake of a French song performed by Claude Francoise “Comme d’Habitude”
On reflection, I’m not sure if this counts, because although the melody is the same, the lyrics are different. (The French song is about a couple that have fallen out of love but continue with their lives together out of habit.)
Not “Cecil’s Terrestrial Music Organization”?
I see what you did there. Eventually.
Similarly, “New York City” is not original to TMBG. I didn’t know that until I saw them in concert and the opening act was a trio from Vancouver called Cub. Someone in the audience called out for “New York City” and they didn’t know if they should, if the headline act was going to play the same song in their set. One of the Johns must have given his approval from offstage, because they did play it.
Cub broke up a few months later; I’m glad I got to see them live.
Today I learned that a song I have heard tons of times, Pills, is not a New York Dolls original. I guess I didn’t look too closely at the song credits on that album.
^“Dazed and Confused” - Led Zeppelin
I never realized that song was a cover.
Sorry about my workaround here. It’s late and I’m tired. I’ll try to better next time. 
Another cover by The Yardbirds.
The original folk-rock “Dazed and Confused” by Jake Holmes…
Wow, I’d never heard of him. Great version too.
It’s amazing as long as that song has been around, and as long as the internet has, that it took so long to learn it was a cover.
All of you late 70s early 80s era hard rockers probably had Nazareth’s Hair Of The Dog in your record collection. I’m aware that Nazareth loved covers (Love Hurts, This Flight Tonight), but was unaware that Beggar’s Day was a cover.
As a longtime Neil Young and Crazy Horse fan, let me tell you that I was surprised to learn just this past weekend that Beggar’s Day was a song penned by Nils Lofgren during his membership in Crazy Horse. It’s on the record Crazy Horse released by themselves with no Neil.
“Barbara Ann”, often considered to be a staple song by The Beach Boys, was actually a cover song originally recorded by The Regents. It was only when The Beach Boys were recording their Party! album that Barbara Ann was recorded, and only then at the request of Dean Torrence of Jan and Dean (who sang lead on the single version).
The Byrd’s “Turn, Turn, Turn” is a cover of Pete Seeger’s version, which in turn was a cover of the song by the Limeliters, which was written by Pete Seeger…
And Pete Seeger’s song was a cover of Ecclesiastes 3:1-8… (-: