Cats have 5 claws on the front feet, and 4 on the rear., so that's 18 claws per cat. ;-) The front feet have a dewclaw, a bit higher up than the pads, much as a dog does.
Our cats are and always have been, indoor-only, (for their own safety), and the claws do not get worn down as they might if the cat were roaming outdoors. It is cruel and barbaric to de-claw cats (see my hub on the subject, '"So you think you want to have your cat de-clawed?" for the full story), so indoor kitties need to have manicures every so often. ;-)