Cats should occasionally decide that they want to go to some normally restricted place. Normally outside, but also sometimes the caverns, the barracks, noble's bedroom, or Hell. They will path to this location and then attempt to hunt vermin. If no vermin are present, they'll instead pick an expensive furniture item to use as a scratching post, headbutt the legs of a dwarf busy with crafting, hauling, or sparring (with a chance for resulting injury, of course), or sit on top of a crafting table rendering it inoperable. If the cat encounters a closed door in its path, it will stop at the door and begin meowing, driving up the stress of all nearby dwarves (and the player, if their speakers are on) until someone opens the door. A cat with high creativity and reasoning attributes may instead jump up to the doorknob and twist it open, leaving the door open for any creature to pass through until a dwarf comes along to secure it again. If the cat is blocked by a drawbridge, same deal except the clever cats will hunt down the lever that opens the door and pull it.
This effectively nerds turtling behind drawbridges, as doing so will inevitably drive your dwarves insane from the constant meowing of cats who want to get outside. The clever cats can also serve as a hidden antagonist, like vampires. Watch your levers well, and keep track of your cats!