Cats that don't grow too big include Teacup cats, Penholder cats, Singapura cats, Munchkin cats, Devon Rex cats, Oriental Shorthairs, European Shorthairs, American Shorthairs, Exotic Shorthairs, and British Folds.

Teacup cats are not an officially recognized breed, but rather refer to a very small breed of cat that is not recognized internationally. Teacup cats are miniature cats, typically only one-third to one-half the size of a regular cat.
The above are just some of the pet cat breeds that don't grow very large.