Some unique breeds of cats include the Sphynx, Bengal, Ragamuffin, Cornish Rex, and Devon Rex. These cats are unique due to their physical characteristics, such as the Sphynx's lack of fur, the Bengal's spotted coat, and the Rex's curly fur. Additionally, these breeds also differ from other cats in terms of their personalities, as some breeds may be more active, intelligent, or affectionate than others.