Cats will kill vermin in and around your fortress. They are fairly weak animals in combat (but combat can be quite random, and they have been known to surprise players on the rare occasion). They also seem to want to wander every room, hall and mineshaft at least once, perhaps due to some modeling of curiosity.
Cats cannot be assigned as pets; instead, cats choose dwarves as owners. Cats randomly choose from all the dwarves on the map, but have a much higher probability of choosing a dwarf who has the preference "admires cats for their aloofness". If a cat is caged, it will not adopt, however it may adopt the moment it is taken from the cage (perhaps to be immediately butchered), regardless of who takes it.
Cats are useful around the fort to prevent the unhappy thoughts produced by vermin, and also for producing large numbers of kittens. If you can resist their cuteness and charm, and you get to them before they adopt a dwarf, kittens can be butchered to provide a small never-ending trickle of skin (to become leather), bones (for a variety of end-products) and meat for your fort. As a breeding pair of cats only costs 22 embark points, this is well worth considering - just cage and/or butcher the kittens as they are born, lest the kittens grow to adopt a dwarf before their last voyage. (See Breeding)
Cats, by nature, will attempt to pack vermin to their owners - often, the owner will then dismiss the cat, at which point the cat will attempt to bring the vermin remains to an appropriate refuse stockpile. However, because they lack body parts that can grasp, they will cancel the task with a "too injured" message, leaving the vermin on the floor for another dwarf to clean up. For more info and a fix, see Cat cancels Store Item in Stockpile: Too injured.
[CREATURE:CAT] [NAME:cat:cats:cat] [TILE:'c'][COLOR:0:0:1] [VERMINHUNTER] [PETVALUE:20] [CARNIVORE][NATURAL][PET] [LARGE_ROAMING] [COMMON_DOMESTIC][BENIGN] [PREFSTRING:aloofness] [BODY:QUADRUPED:TAIL:2EYES:2EARS:NOSE:2LUNGS:HEART:GUTS:ORGANS:THROAT:NECK:SPINE:BRAIN:MOUTH] [BODYGLOSS:PAW] [SIZE:3] [MAXAGE:10:20] [ATTACK:MAIN:BYTYPE:MOUTH:bite:bites:1:6:GORE][ATTACKFLAG_CANLATCH] [CHILD:1][CHILDNAME:kitten:kittens] [FAT:1] [DIURNAL] [STANDARD_FLESH] [HOMEOTHERM:10070] [LAYERING:100] [SWIMS_INNATE][SWIM_SPEED:2500] [MUNDANE]