Polydactyl Cats
Several populations of cats regularly produce individuals with polydactyly, a.k.a. extra toes (the usual number for cats being five toes on each front foot and four on the back). Polydactyl cats have between 1 and three extra digits on any given paw. This phenotype was recognized and discussed by Charles Darwin as an inherited trait.
Many breeders avoid mating two polydactyl cats, but those who have done so report no problems. Polydactyly is considered a harmless mutation and so something a responsible breeder can selected and breed to promote if thy like the look of it. Historically cats with polydactyly have been referred to as mitten, boxing or thumbcats.
Hemingway Cats
Hemingway house is home to a population cats about half of which have an extra toe on their front paws. They are descended from a polydactyl cats called Snowball who was given to Earnest Hemingway. Most have six toes on their front paws.
Snowshoe Cat
Polydactyl Maine Coons are also known as snowshoe cats. Like Hemingway's Snowball they have a link to cats favored by sailors. The polydactyl gene was present in the breed during its early development in the state of Maine. (C.f. white footed cats by the same name.)
Pixie Bob
The only currently recognized breed that allow extra toes is the Pixie Bob.This breed is reputed to descend from barn cat x bobcat matings but such a combination is biologically unlikely and not objectively confirmed. A pixie bob may have 6 or seven front toes.
American Polydactyl Cat
The American Polydactyl Cat is breed specifically for the extra toe trait with the goal of developing a recognized breed.
Munchkin Cats
Munchkins are cat with short front legs, they also sometimes show polydactyly.
Others
Extra toes have also been documented in a number of breeds in which is is considered a deformity to be avoided, including Bengal. It is also not particularly uncommon in mixed breed cats.
Polydactyl Traits
Some suggest that extra toes may be linked to genes that cause harmful abnormalities in the legs sometimes referred to has "twisty cat". However, most breeders consider the trait harmless. In fact, many consider that polydactyl cats bring good luck to a home.
Memes
Cats with thumbs appear in many popular memes including: