How many cat colors are there?

Cat colors nearly always relate to cat breeds as opposed to species. If the question means "How many cat colors and pattern combinations are there for the cat breeds" (which is what I think the question means) the answer, per Gloria Stephens in her excellent book: legacy of the cat (lower case title) is....144...Hope this helps :)

If the question is purely about cat breed coat colors I don't know the answer because the question might be too tricky to answer bearing in mind that color types are dictated by the cat associations of which there are several. They can have different ideas. Comments welcomed ;)

Sorry for the weak answer. I am watching the men's final at Wimbledon 2016 while writing this... :)