General:
* Cat
* Feline
* Kitty
* Pussycat
* Moggy
* Tabby
* Tomcat (male)
* Queen (female)
* Kitten (young)
Appearance:
* Calico
* Siamese
* Persian
* Maine Coon
* Sphynx
* Short-haired
* Long-haired
* Black
* White
* Grey
* Ginger
Personality:
* Hunter
* Playmate
* Companion
* Pet
* Cuddlebug
* Independent
* Mischievous
* Lazy
* Grumpy
* Affectionate
Other:
* Litter
* Clan
* Colony
You can also use metaphors to describe a cat:
* Shadow
* Sunbeam
* Puppet
* Ninja
* Leopard
* Lion
The best noun to use will depend on the context and the specific cat you are describing.