The term hypoallergenic and non-shedding is often used to describe certain breeds of cat; but, there are no cat breeds that are non-shedding, and there is no such thing as hypoallergenic. There are, however, cat breeds which have only a low amount of shedding which is consequently good for those suffering from pet allergies.
Bengal Cat: The silky pelt-like coat of the Bengal cat is not only beautiful to look at and nice to touch, but it also has minimal shedding. The coat of the Bengal is also very short which makes for easy grooming.
Bombay Cat: The Bombay cat has very little to no shedding, and produces very little dander, which is the main allergy trigger when it comes to cat allergies.
Colorpoint Shorthair: The easy-to-care-for coat of the Colorpoint Shortair is low shedding, and only requires little grooming—brushing twice per month to remove dead hair will virtually eliminate shedding.
Cornish Rex: The wonderfully textured coat of the Cornish Rex is short and sparse, which makes the breed susceptible to cold weather.
Abyssinian: The Abyssinian breed tends to shed less than other cat breeds, and has a coat that is easy to care for and only needs weekly brushing to remove dead hair which will reduce shedding even further. Baths, as necessary, during shedding will virtually eliminate any loose hair problems.
British Shorthair: The British shorthair has an easy-to-care-for coat which only requires a weekly brushing, but during shedding season (spring) more frequent brushing will be necessary to remove excess dead hair.
LaPerm: The coat of the LaPerm is very similar to that of the Poodle (curled), which prevents most shedding hair from falling off. Regular brushing will remove the dead hair which will reduce shedding even more.
Siamese Cat: The very short hair of the Siamese Cat is easy to groom, and sheds much less than other breeds on average.
The best way to be sure that there is no shedding from your house-cat is to have a hairless cat as part of your household. The hairless cat breeds may not look as cuddly as those with a plush coat, but they can still be affectionate and loving companions, and they have the added benefit of not peppering the entire house with tiny little hairs.
Do note that just because they are hairless it does not mean that they do not produce dander, so they can still cause allergic reaction in people who are highly sensitive to cat dander.
Having a pet in the house, regardless of the size, the amount of hair, or drool will have a noticeable impact on living conditions, and in order for owners to maintain a hygienic environment, it will be necessary to be more vigilant and clean more often.