Today there are four breeds that are recognized internationally by at least one major kennel club that are hairless, the aforementioned American Hairless Terrier (AKC, UKC), Chinese Crested Dog (AKC, FCI, KC, UKC), Peruvian Inca Orchid (FCI, UKC), and the Xoloitzcuintli (AKC, FCI, KC, UKC). The Peruvian Inca Orchid (also known as the Peruvian Hairless) and Xoloitzcuintli (or Mexican Hairless) are both ancient breeds, while the American Hairless Terrier was not created until the 1970s. As for the Chinese Crested, well, that is where most of the debate lies.
Hairless dogs have existed in Central and South America since before written record, even today there are several breeds such as the Argentine Pila and Bolivian Khala that are unrecognized that still survive in more remote areas of the South American continent. As a group archeological evidence shows they have existed since at least pre-Colombian times and may date back for more than 3500 years. How they came to the area is debated, but in appearance they hold true to a more primitive type of dog, similar to the Carolina Dog of the United States and those traditionally kept by Native Americans that are now lost to us.
For decades dog fanciers have insisted that the Chinese Crested and the American breeds have to be closely related due to their hairlessness. Many believe that the Chinese Crested is the older of the two, some even going so far as to assume that the Chinese brought hairless dogs on sea voyages to the new world long before Columbus himself stepped onto its soil. According to these beliefs the Chinese Crested descends from African hairless dogs (although others have held firm that again the Crested is the older of the two) spreading out from Africa to Asia long before written record.
Despite the commonly accepted theory that Chinese Cresteds were transported by Chinese sailors around the world (supposedly their presence on ships was to help control the rat population) there is no mention of hairless dogs in China prior to the 16th century. As to the Chinese Crested being the basis for all hairless breeds there is no record of any hairless being imported from China. It seems far more likely that the primitive Xoloitzcuintli and its ancestors spread first throughout Central and South America, and after the discovery of the New World, onto Africa and from there Asia and Europe. There are records of hairless dogs being transported and traded throughout all the major trade routes during the 17th and 18th centuries. With this knowledge, it is quite possible the now extinct hairless “breeds”, such as the Abyssinian (also known as African) Sand Dog and Egyptian Hairless may very well have been nothing more than decedents of Xolo-type imports.
This still leaves us asking where the Chinese Crested originated and what little evidence we have points to the United States. Early prototypes of these dogs appeared in the 1800s, but no stud books or records exist to point as to where they came from. It appears that they are the result of crosses of Xolo-types with terriers and Chihuahua-type dogs. True records were not kept until the 1950s when Debora Wood began doing so at her Crest Haven Kennel. Although where she obtained her base stock, is not recorded it is from Crest Haven that nearly every line of Chinese Crested can be traced back to. Still the Chinese legends persist, and it is doubtful they will ever be put to rest with nearly every kennel club and breed book continuing to state them as fact.
If you would like more information on the hairless breeds I recommend picking up the book Hairless Dogs, the Naked Truth by Amy Fernandez and Kelly Rhae.