Here's a list of cat breeds from one of the largest breed registries in the world, the CFA.
There are a number of organizations and governing bodies of the cat fancy worldwide, and the CFA is one of the best known.
Each registry has its own requirements and breed standards, thus making the lists from the various organizations different.
From time to time, new breeds will be recognized.
Sometimes, this is a matter of recognizing a variant of an existing breed. Other times is just a matter of a coat color or length that was previously not allowed.
The Javanese, for example, is a version of the Balinese, but with non-traditional Siamese coloring and patterns.
The CFA breed standard is the same for the two cats, except for the colors and patterns that are allowed for competition. The CFA merged the breeds in 2008.
Similarly, the Somali is essentially a long haired Abyssinian. Not so similarly, however, these cats are registered and shown as two separate breeds.
At times, breeders will create a new breed that is quite different from the ones it's created from. It takes time for the breed to develop, and even more time for the characteristics to be considered stable from generation to generation.
Then, an association has to accept the breed and subsequently, the breed is added to the list of breeds for that particular association.
The Cat Fanciers' Association (CFA) is the "World's Largest Registry of Pedigreed Cats." As of this update, it recognizes "42 pedigreed breeds for showing in the Championship Class" and one in the Miscellaneous Class (the Bengal).
The addition of the Bengal cat is significant because prior to April, 2016, none of the cats in the CFA registry were hybrid cat breeds.
This is a noticeable difference between the CFA and some other organizations in the Cat Fancy, such as The International Association of Cats (TICA). TICA has several hybrid cats in its ranks.
Hybrids are a cross between a wild cat and a domestic cat. In the case of the Bengal, it's a cross between the Asian leopard cat and a domestic.
There is a lot of controversy surrounding hybrids. On one side, breeders and enthusiasts meow their praises. On the other, detractors warn of unpredictable personalities and bad behavior, as they pass local laws banning them.
In some ways, hybrid cat breeds are symbolic of the bigger war between those who see the benefits of breeding, and those who are against breeding altogether.
When choosing from among the different cat breeds, it may be helpful to review the breed profiles so you know more about what to expect from a particular breed (Persians need lots of grooming, Siamese are very talkative and active, etc.).
The CFA breed list is below (current as of this writing). Click the links below to read more about each type of cat.