I'm just wondering which songs should never be covered. But they probably already have.
Ones that immediately come to mind.
When Doves Cry - Prince
Rum and Coca Cola - The Andrew Sisters
Some of David Bowie's early/mid 70s stuff.
Changing gear somewhat, by far Australia's best cover band was the Iva Davies led Flowers who went on to become Icehouse.
I saw them over 30 times in the Sydney southern/eastern suburb pubs from the late 70s until they commercialized and become Icehouse. Places like Selina's, Sylvania, Caringbah Inn were the days.
Covers of Bowie, Iggy Pop, Lou Reed, Ultravox, Roxy Music, Brian Eno, T-Rex/Marc Bolan (took me a million years to track down a copy of Bolan's Think Zink), Sex Pistols amongst a bunch more were just incredible. The most memorable cover was of Ultravox's Frozen Ones where Davies just completely deconstructed and reconstructed the song with such sterility that the original sounds like shit.
End of self indulgent memories....lol.