Some of the most unique breeds of cats include the Bengal, the Savannah, the American Curl, the Toyger, the Lykoi, and the Sphynx. The Bengal is a hybrid breed that is a mix of domestic cats and Asian leopard cats. The Savannah is a hybrid breed that is a mix of domestic cats and servals. The American Curl has distinctive ears that curl back towards its head. The Toyger is a breed that has been bred to look like a miniature tiger. The Lykoi is a breed that is known for its wolf-like appearance. The Sphynx is a breed that is known for its hairless appearance.