Songs like My Way (made most famous by Frank Sinatra, lyrics by Paul Anka, also recorded by Elvis Presley... set to the music of a French song Comme d'Habitude which was a hit for Claude Francois). Songs like those written by Randy Newman, which were covered by Gene Pitney--a wonderful singer-songwriter who wrote songs for others such as Roy Orbison and The Crystals, while himself recording songs by Burt Bacharach and Hal David as well as Randy Newman). Popular TV variety shows would showcase many, many cover versions by performers who were very well known.
As a kid, it was never obvious which song "belonged" to which singer. One song that I adored though was "I Who Have Nothing. An English-language version of the Italian "Uno Dei Tanti" (direct translation: One Of Many), music by Carlo Donida, lyrics by Guilio Rapetti, with the English words written by Jerry Lieber and Mike Stoller. The first English-language version was recorded by the American Ben E King (The Drifters), but was better known in the UK through cover versions by Tom Jones and--the one that has always been my go-to version--Shirley Bassey. The name of the song and the name Shirley Bassey are inseparable in my memory... despite so many, many other cover versions.
Ben E King, Tom Jones, Joe Cocker. Neil Diamond.
Roberta Flack and Donny Hathaway
Liza Minelli, Donny Osmond.
It's often heard on TV talent shows, to greater or lesser success.
Sylvester released a disco version (really, really don't go there)
Definitely... Shirley Bassey's was my lifelong favourite version, of a lovely, lovely song. That is, until I heard this. This version, by Bloodshake Chorus.