Some of the most unique and interesting breeds of cats include the Sphynx, the Bengal, the Maine Coon, and the American Curl. The Sphynx is known for its hairless coat, the Bengal for its wild-looking markings, the Maine Coon for its large size, and the American Curl for its distinctive curled ears. All of these breeds are unique in their own way, and they are all sure to be a conversation starter.