Some of the most trainable animals as pets include dogs, cats, birds like parrots, and certain small mammals like rabbits and rats. Dogs are often considered the most trainable due to their intelligence and ability to learn commands and tricks. Cats can also be trained to some extent, especially with positive reinforcement techniques. Birds like parrots are known for their ability to mimic sounds and learn tricks. Small mammals such as rabbits and rats can also be trained using positive reinforcement methods.