Bubka, why would you even ASK such a thing?!? Killing animals simply for the sake of killing is CRUEL. Hashem teaches us that we need to have respect for ALL creation, including animals. I’m fairly certain that the ONLY, and I repeat ONLY times you should be killing animals is if they are sick/injured and suffering to the point where you cannot heal/cure them in any way, and to release them from their pain, OR, if the animals are kosher and you’re going to shecht them for Jewish consumption, but of course this does not apply to cats. yytz said it more succinctly than I did.
Uneeq, you’re forgetting that those “filthy” cats that are homeless and running feral around Jerusalem, were once brought in to kill infestations of rats and mice. If someone were kind enough to spay/neuter many of them, as well as give them homes, you won’t have to deal with them. On the other hand, if you don’t like cats, just move away from them.