Catman is a parody of Batman which the real-life Adam West played in the 1960s. There is also a Catman villain in the Batman universe who uses the same orange and yellow costume as this Catman.
When he was young, Adam West acted as Catman, but when he was older, he portrayed the Crimson Chin, this might mean that Adam West might be a multi-tasking actor.
Despite being portrayed as incompetent and "washed up", he seems to be very rich and hired Vicky to do his chores and paid her a load of cash.
He would have gone to jail if Timmy didn't wish that he was innocent for injuring a janitor near Mrs. Turner at a supermarket.
As he is a legal guardian of Timmy Turner, he can be considered an unofficial member of the Turner family.
Jeff Bennett, Catman's replacement voice actor following the death of Adam West, was the voice of the titular protagonist on Johnny Bravo, a show that Butch Hartman worked on during the first season before creating the Fairly OddParents. Adam West also guest-starred on Johnny Bravo in the first season as himself.
Until Season 9, the series made it clear that he and Adam West were the same person, but in "Whittle Me This" (a Season 10 episode), Timmy just refers him as "just some crazy actor". This might be a reference to his new voice actor, Jeff Bennett.