Some dogs that don't shed much include the bichon frise, havanese, Italian greyhound, toy poodle, Irish terrier and standard poodle. A more complete list of dog breeds is available on DogChannel.com.
These dogs, considered to be hypoallergenic, are often quite sought after for housekeeping and allergy purposes. Less shedding typically results in less dog hair spread around the house, and less shedding also generally indicates less allergen production.
Dog hair is not what sets off allergies, actually. Dog dander, or the dead skin that falls off of dogs, is actually the culprit; it deposits around the house and gets airborne. Dogs that don't shed a lot produce much less dander than other dogs. Dogs with a thick coat, generally the ones responsible for more shedding, also tend to attract pollen and transfer it from outside into the house.
Responding to the popularity of dogs that shed very little, dog breeders have created hybrid, or designer, dogs. Popular dog breeds that tend to shed a lot are bred with poodles in hopes of transferring the Poodle hair gene. This is not an exact science, however, and the poodle hair gene does not always prevail. These designer breeds include the labradoodle and cockapoo.