The legality of owning certain animals as pets can vary depending on the country, state, or city regulations. Common pets that are legal in many places include dogs, cats, fish, birds (such as parrots and canaries), small rodents (like hamsters and guinea pigs), rabbits, and reptiles (like turtles and snakes). However, it's important to check local laws and regulations before acquiring any exotic or unusual pets, as some species may be restricted or prohibited for private ownership.