A cat is considered to be of a certain breed if it is true breeding for the traits that define the breed. Cat registries are the ones who determine which traits that define a breed, and also which traits that are especially valued or shun. A true breeding cat (also known as a pure-bred cat) will pass on certain biological traits, e.g. body type, to all subsequent generations if it is bred with a true breeding mate belonging to the same breed.

Please note that cat type is not the same thing as cat breed. Examples of cat types are dwarf cats, longhaired cats, shorthaired cats, and squittens. A cat can belong to several cat types simultaneously, e.g. if it is a short-haired dwarf cat. A true-breed cat can also belong to a certain type, e.g. a Siamese cat that belongs to the short-haired cat type.   

Today, roughly three percent of pet cats are believed to be pure-bred cats and the figure varies greatly from country to country. Most cat shows will not allow a cat to enter a show without a registration certificate that proves to which breed the cat belongs and shows the family tree of the cat going back at least four generations. In a cat show, the winner is the cat who is closest to the definition and standard of the breed.

There are many different breeds of domestic cats and different cat registries acknowledge somewhat different breeds. Most registries acknowledge about 30-40 breeds, but that number is believed to increase in the future as more and more breeds are recognized around the world.
Below you can find a list of breeds recognized by The International Cat Association (TICA). TICA is the world's largest genetic cat registry and one of the world's largest sanctioning bodies for cat shows.

The breed ideal, as defined by a cat registry, can be found in the breed standard. Each recognized breed has its own breed standard. If you for instance look at the TICA breed standard for the Siamese cat, you will learn that the Siamese cat “is a medium-sized shorthair, pointed cat, oriental in type”. You will also see that its eyes should be “almond-shaped, mediumlarge, set with an Oriental slant toward the nose such that a line from inner corner through outer corner is in line with center of base of ear”, that the ears should be “wide at base, strikingly large. Set to continue the line of the wedge; neither too high nor too flared”, and so on. For almost every physical trait, the breed standard will contain a description of the ideal towards which cat breeders are encouraged to strive.

It is also common for breed standards to contain ideals for non-physical treats, such as the temperament of a certain cat breed. The TICA breed standard for the Somali cat does for instance say that the “temperament must be unchallenging; any sign of definite challenge shall disqualify. The cat may exhibit fear, seek to flee, or generally complain aloud but may not threaten to harm”.

List of cat breeds recognized by TICA
Abyssinian
American Bobtail
American Curl
American Shorthair
Balinese
Bengal
Birman
Bombay
British Shorthair
Burmese
Chartreux
Chausie
Cornish Rex
Devon Rex
Donskoy
Egyptian Mau
Exotic Shorthair
Havana
Highlander
Himalayan
Japanese Bobtail
Korat
Kurilian Bobtail
LaPerm
Maine Coon
Manx
Minskin
Munchkin
Nebelung
Norwegian Forest Cat
Ocicat
Ojos Azules
Oriental
Persian
Peterbald
Pixiebob
Ragdoll
Russian Blue
Savannah
Scottish Fold
Selkirk Rex
Serengeti
Siamese
Siberian
Singapura
Snowshoe
Sokoke
Somali
Sphynx
Thai
Tonkinese
Toyger
Turkish Angora
Turkish Van

Some cat breeds are the result of hybridization between the domestic cat and a wild feline, such as the Bengal cat which is a hybrid between domestic cat (Felis catus) and Asian Leopard Cat (Prionailurus bengalensis). A few other examples of such hybrids are:

• Bristol                     domestic cat x Margay (Leopardus wiedii)
• Chausie                   domestic cat x Jungle cat (Felis chaus)
• Cheetoh                  domestic cat of the Ocicat breed x the hybrid Bengal
• Punjabi                    domestic cat x Indian Desert-Cat (Felis silvestris ornata)
• Safari                      domestic cat x Geoffroy's Cat (Leopardus geoffroyii)