Until 1975, when they were banned for hygiene reasons, it was common practice for Royal Navy ships to sail with a cat aboard. The cat was useful in keeping down the ship's rat and mouse population, and provided a mascot for the crew. This practice didn't change in wartime.

One example of a ship's cat in a war zone was Simon, the cat of the RN sloop HMS Amethyst. In 1949, Amethyst was transiting the Yangtse between Shanghai and Nanjing. She was to become guard ship for the British embassy in Nanjing, which was threatened by the ongoing Chinese Civil War. While she was travelling, she came under fire from PLA shore batteries. The bridge received several hits, and due to this she ran aground. She was refloated quickly, but was unable to move due to the shore batteries. Amethyst remained stuck for three months, before finally making her escape. Simon was wounded in the initial exchange of fire, but was given medical attention and made a quick recovery. During the period when Amethyst was stuck, Simon was highly useful at catching rats and helped keep the crew's morale up.

Commodore MacDonough had a fighting gamecock (a Blue Hen breed rooster, the state bird of his native Delaware) aboard the Saratoga during the war of 1812: http://www.battleofplattsburgh.org/blog/?page_id=173

See also http://en.wikipedia.org/wiki/Ship%27s_cat#Early_history - the ship's cat has a history going back to ancient Egypt