“Sh-Boom” was a hit for the Chords in March 1954; the Crew Cuts did a version that came out in July and went to number 1.
It was very common in the 50s for white artist to cover songs by Black artists, often while the originals were still on the R&B charts. Pat Boone made a career out of it.
The Beatles released “Let it Be” 2 months after Aretha Franklin released her version.
Chaz Jankel and Kenny Young wrote “Ai No Corrida” for Jankel’s 1980 debut album as a solo artist. “Ai No Corrida” was selected as the first single and was released in August 1980.
Somewhere, Quincy Jones heard Jankel’s single and thought it could be a big hit in the U.S. Jankel’s single didn’t chart in his native UK, but it was a hit in Belgium. Accordingly, my pet theory has always been that one of Jones’ long-time collaborators, Belgian multi-instrumentalist Toots Thielemans, introduced Jones to “Ai No Corrida”. Thielemans was one of the session player on Jones’ upcoming album The Dude at around this time.
Anyway, Jones released “Ai No Corrida” as a single in the US in April 1981. It hit #28 on the US Hot 100, and was Top Ten on both the US R&B chart and the US Dance Hits chart.
I thought it all happened more closely in time, but Prince wrote “Nothing Compares 2 U” for his side project band The Family in 1985.
Then Sinéad O’Connor made the song a huge hit when it was released as a single in 1990.
Finally Prince released his own recorded version on " The Hits/The B-Sides* in 1993.
I was expecting a half dozen or so.
I’m not sure I count the Monkees though. Or Three Dog Night had they been mentioned.
Memories of Casey Kasem on “American Top 40.” 
Little Steven is great at spinning tales like this, too. I once heard a full set of the different versions of "Hey Joe’ from 1966 on his show.
“Torn” by Ednaswap was released in 1995 but I only remember it getting airplay once Natalie Imbruglia’s 1997 cover became huge.
Dylan had written (in early 1964) and recorded the song (one of his masterpieces, btw.) in June 1964, and knew that it was an important song, but wasn’t contented with the first recorded version and re-recorded it for “Bringing It All Back Home”.
[Tangent]
A question I’ve had for years is “how many songs can one play on a tambourine if that’s the only instrument around?”
I mean, there are thousands of songs that are easily recognized by the guitar riffs or the piano or bass. But I’m imagining trying to play Name That Tune using just the tambourine, and I got nuthin’.
[/Tangent]
Petula Clark and Andy Williams both had a hit with Happy Heart in 1969.
Of course the tambourine mostly is the instrument you put into the singer’s hands so the they have something to do with their hands, but it can be a VERY effective instrument. The Motown sound is unthinkable without the use of the tambourine.
But how many songs can you name just by hearing the tambourine? Even in Motown, it’s not a solo instrument.
Green Tambourine
Percussive instruments generally aren’t lead instruments.
And somebody else did it before then. Ednaswap’s version is the best, by far. I’ve posted this a hundred times on this board. Well, maybe 4 times.
The one that comes to mind is the song ‘Tomorrow Wendy’ written by Andy Prieboy, ex-Wall of Voodoo. His version features Johnette Napolitano on vocals, and her band Concrete Blonde released their own cover, which came out before his album or single were released.
Privileged to see both renditions live. Hard call but Andy Prieboy’s live version was better.
An interesting case is the great New Wave/Punk classic “Ca Plane Pour Moi”. It was first released by Plastic Bertrand in 1977, and a short time later Elton Motello released it with different (English) lyrics, using exactly the same backing track:
The Damned also did it around that time, but recorded the backing track themselves:
I’m kind of surprised no one mentioned “Blue Suede Shoes” yet. Carl Perkins recorded the song in 1955 and earned a gold record with it, and then Elvis Presley recorded the more well known version of it in 1956.
Would Stan Freberg be a third artist?