In general, they make engaging pets, but require owners with the determination to match their dogs’ lively characters. Airedale Terrier. American Hairless Terrier. American Staffordshire Terrier. Australian Terrier. Bedlington Terrier. Border Terrier. Bull Terrier. Cairn Terrier. List of Terrier Breeds 1 Border Terrier 2 Borzoi Terrier 3 Boston Terrier 1 Border Terrier Possibly one of