"The Persian Kitty" has always been one of my favorites and Weird Al did one called the "Cats In The Kettle". Andrew Lloyd Webber and T.S. Eliot combined forces for a number of songs about cats including the following:

Naming of Cats
Old Gumbie Cat        
Rum Tum Tugger
Grizabella
Old Deuteronomy
Macavity
Mr. Mistoffeles