The legality of owning certain pets can vary depending on location. In general, some pets that are commonly illegal to own in many places include big cats (such as lions, tigers, and leopards), primates (such as monkeys and chimpanzees), certain reptiles (such as alligators and venomous snakes), and exotic or endangered species. It is always recommended to check with local authorities or animal control to determine which pets are legal to own in a specific area.