Cat breeds that don't shed as much tend not to be as popular or well-known as common house cats, but there are a number of them, including Rex cats and certain European and Asian breeds. Cats that don't shed much are known as hypoallergenic cats. While no cat is completely non-allergenic, there are a number of cats that don't shed enough to cause an allergic reaction in most people.
Cats that don't shed much are quite common. Popular breeds include the Sphynx, the Devon Rex, Korat Cats, the LaPerm, Tonkinese cats, the Turkish Angora, the Cornish Rex, the European Burmese, the Turkish Van, the Ocicat, the Bengal, the Singapura, the Bombay, the Burmese, the Colorpoint Shorthair, the Siamese, the Balinese, the Javanese, the Oriental Shorthair, the Russian Blue, and Siberian cats.
There are also hairless cats, which have coats made of very short hairs. These cats do shed a little, but the shedding is unnoticeable due to the shortness of the hairs and how sparse the shedding is. The shedding of a cat is typically based on how many layers of coat the cat has. Typically, there are three layers: guard hairs on top, awn hairs in the middle, and down hairs as the undercoat. The fewer layers of coat, the less the cat will shed. Hairless cats and short haired cats generally have less hair and therefore naturally shed less.