The 10 rarest cat breeds in the world include American Wirehair, Burmilla, Chartreux, Cornish Rex, Egyptian Mau, Korat, Kurilian Bobtail, LaPerm, Minskin, and Sokoke. Among these, the Sokoke cat from Kenya is considered the rarest domestic cat breed, known for its unique ticked tabby coat and tip-toe gait.