That Cat Is High Originally The Ink Spots (1938), but a nice version from the band who was officially promoted as "the loudest jug band in the world" - The Captain Matchbox Whoopee Band (Melbourne's original stoners, from 1973). (and the song's not really about felines)
Les Paul & Mary Ford/ Tiger Rag (love Mary Ford's witty choruses, "Meow, Here Kitty Kitty, Here Kitty Kitty Kitty, Here ***** ***** *****")
As a cat lover, I wish this thread were actually collecting songs about felines and not just songs that mention the word 'cat' (or any other breed of cat, large or small). Most of these songs are really just about sex or the other usual subject matter. Here's one that is actually about a cat: 'Man from Mars' by Joni Mitchell A song written about Joni's tomcat Nietzsche after he ran away. (Don't worry, he came back).
Not really songs....more like an album art mystery. Iron Maiden: The Legend of the Black Cat – Green and Black Music