Humans are the only animals to have invented computers, and no animal uses them in nature. Some mammals can be trained to use computers, however, and some non-human primates regularly use them for communication and recreation.
Chimpanzees under study in Japan as part of the Ai Project regularly use computers with touchscreen interfaces to play complex memory and number games, according to Ella Davies Anna-Louise Taylor, writing for BBC Nature. The computers were installed near the chimps' enclosure as a way of studying their learning abilities and to relieve some of the stress of captivity.
According to Wikipedia, computer keyboards, along with sign language, are often used for communicating with study animals. A computer's tactile interface permits non-verbal communication, overcoming the anatomical limitations of apes' mouths and throats.