Pets allowed in rentals are typically determined by the landlord or property management company. Common pets that are permitted in rental properties include cats, small dogs, fish, birds, and small rodents like hamsters or gerbils. Some landlords may have restrictions on the size or breed of dogs allowed, while others may prohibit certain exotic pets or reptiles. It's important to check the lease agreement or speak with the landlord or property manager to understand the specific pet policy for a rental property.