The legality of owning certain pets can vary by region, so it's essential to check the local laws and regulations in your area. However, some common examples of pets that are often illegal to own include big cats (such as lions, tigers, and leopards), primates (such as chimpanzees and monkeys), exotic reptiles (such as alligators and venomous snakes), and certain bird species (such as birds of prey). It's important to research and adhere to the laws regarding pet ownership to ensure the well-being of both the animal and the owner.