The answer to this question is a very qualified "yes." Hypoallergenic dogs certainly exist, but one must realize that hypoallergenic means "less allergens," not "no allergens." All dogs produce dander, the main culprit in dog allergies, to some degree, and a dog's saliva and urine can also cause allergic reactions. Dander includes shed fur, but also flakes of dried skin. It is similar to dandruff in people. People who are very allergic or who suffer from severe asthma may still be unable to coexist with hypoallergenic dogs.
The degree to which any dog is likely to cause allergies is a result of its coat type. In general, hypoallergenic dogs may have one of two coat types. "Single-coated" hypoallergenic dogs differ from regular dogs in that they do not feature a thick under-layer of fur, which is responsible for most of the dander that causes allergies. "Hairless" breeds produce even less dander, but it may still be enough to bother someone with intense allergies.
A few single-coated hypoallergenic dogs are the Poodle, the Powder Puff Chinese Crested, the Schnauzer, and the Bichon Frise. Recently, the Poodle has become an option for disabled people who need guide dogs but suffer from dog allergies. Hairless hypoallergenic dogs include the Xoloitzcuintle or Mexican Hairless, the Hairless Chinese Crested, and the American Hairless Terrier.
Even with hypoallergenic dogs, owners who suffer from allergies will probably benefit from reducing allergens in the home as much as possible. Keeping your dogs out of the bedroom and washing your hands after touching your pets are great ways to start. Also, avoid carpets, draperies, and Venetian blinds, as these all tend to collect dust and dander. Keep your home aired out as much as possible.
Even hypoallergenic dogs should be brushed and washed once a week or so, outside the home if possible. Feeding your dog a balanced diet with moderate natural fats can help prevent dry skin and minimize dander. Both your bedding and the dogs' bedding and toys should be washed frequently. You can further prevent dander in the bedroom by placing a cheesecloth screen over bedroom vents.