Some airlines do permit a limited number of animals to be brought on board either as an extra carry-on item or checked in the cargo area of the aircraft. Please contact the airline(s) you're flying with directly well before your scheduled departure date to reserve your pet on the plane (when applicable) and pay any additional fees that might be applicable.
U.S. and Canadian airlines are required to accept trained service animals, although in most cases they are not permitted to occupy a seat. Contact the airline well before your scheduled departure to advise them that you'll be boarding with a service animal, as you may need to provide documentation in order for the service animal to board.