It's not so hard to figure out.
- * Cats are cute (and I don't mean that in a sexual way, although they are graceful).
* Girls are cute (in more than one way).
Put them together: double kawaii [http://en.wikipedia.org/wiki/Kawaii]!
Of course, cat girls are just a small number of strange girl deviations you'll find in anime. Other common deviations are maids, robots, demons, angels, other supernatural, glasses, lolicon [http://en.wikipedia.org/wiki/Lolicon], airheads, authoritative, incestuous, nuns, aliens, ghosts, ninjas, military, scientific, magical [http://en.wikipedia.org/wiki/Magical_girl], Moe [http://en.wikipedia.org/wiki/Moe_%28slang%29], Bishōnen [http://en.wikipedia.org/wiki/Bish%C5%8Dnen], combinations of these (robot maids being common) and more. Basically anything that could be considered exceptionally kinky to someone, not uncommonly because it's a forbidden fruit of sort.
Although it is actually fairly rare to see animal girls that are not cat or bunny girls in anime. Probably because these are related to things girls can wear in their hair to play the part.