If you saw this in a desert wasteland, admit it: You'd run screaming.
There are many breeds of hairless dogs. A large portion of them, including the African hairless breeds, are officially extinct.
A fair amount of hairless breeds still remain. The three that most people know about are the Chinese Cresteds, Peruvian Inca Orchids, and Xolos (AKA Mexican Hairless), but there are a few others, such as the American Hairless Terrier. The Chinese Crested in particular has been a strong contender in "World's Ugliest Dog" contests. (There's a nice video with them here, but just as funny are the links to a Katy Perry interview.)
All hairless dogs come in a haired variety. The trait for hairlessness is lethal if two of the same allele is present; the haired version is recessive in its presence. Therefore, all hairless dogs must be heterozygous for both hairy and hairless puppies.
This is a Chinese Crested WITH fur. They call it a powderpuff.
Along with lacking fur, hairless dogs always have some version of odd dentition (as noticed by Darwin). It is usually not present in their rr haired counterparts. Other health disorders vary with the breed; for example, the Xolo has almost no breed defects beyond dentition, but the Chinese Crested suffers from all the same ailments as other toy dogs.
One allele leads to an impressive creature! There is some general appeal in owning a hairless dog, but the Central American varieties have some particularly interesting lore associated with them. More on that in...well, you'll see.