You could spank your monkey in Black & White :lol: Oh, and the most annoying animal-related thing in a game was in Sacrifice. Hearing "your creatures are under attack!" every 10 seconds - grr!
As well as using cats as silencers in Postal 2, I'm pretty sure you also set them on fire (as well as using all of the other weapons on them, naturally). They go crazy when alight. In the expansion pack, you can cut the legs off of elephants and smash off cows' heads with sledge hammers. Infact, those are actual mission objectives. I'm sure there are plenty more which I'm forgetting. In the original, you can set herds (or whatever the term may be) of ostrich on fire with the napalm gun thing. Man, the noise they make is hilarious. It never gets old...