While there's a lot of debate on the subject, technically truly hypoallergenic dogs don't exist. BUT there are certain breeds like the Coton de Tulear (and others listed below) that are considered to be a good choice for allergy sufferers because they shed very little and produce less of the offending dander.
Early fox terriers were primarily smooth-coated, but the wire coat persisted. By the end of the 19th century, smooth and wire-coated Fox Terriers were in great demand, both as companions and show dogs. Although considered one breed for many years, interbreeding of Smooth Fox Terriers and Wire Fox Terriers ceased in the early 1900s.
Havanese organizations, such as the Havanese Club of America, monitor genetic issues to prevent propagation within the breed. Hypoallergenic: Yes: Intelligence: 2 stars Ranking: (#). (See All Rankings) Playfulness: 4 stars: Shedding Level: 1 stars Minimal Shedding: The Havanese is referred to as a non-shedder, but all dogs shed at least a little bit.
Technically, there are no 100 percent hypoallergenic domestic cats or cats that are completely non-allergenic. All cats produce some amount of dander, so you won't find a dander or allergy-free cat. However, there are breeds that produce less of it and therefore make good cats for people with allergies.