No dog is completely non-shedding, but some breeds drop less hair than others. It's important to note that even low-shedding dogs aren't hypoallergenic as their dander -- or dried skin cells -- and saliva can also cause allergies. While there's no one breed of dog that sheds the least, a range of contenders exist.
The obvious choices for dogs that shed the least are hairless varieties -- if you don't have any hair, you can't shed it. However, they're still low-shedding, rather than non-shedding, as almost all hairless dogs still have a small amount of fur. The closest examples are the Peruvian Inca orchid and the Mexican hairless, but even these may have a small amount of hair on their feet, heads and tails. Other hairless or semi-hairless breeds include the Chinese crested and the American hairless terrier. It's worth noting that some of these breeds come in both hairless and coated varieties.
A fairly large amount of small dogs have low-shedding coats. Bedlington terriers have coats that don't shed naturally, but they do need brushing a few times a week to stop their coat tangling, along with the odd trim. Other small breeds that don't shed a lot include Italian greyhounds, dachshunds, toy poodles, wirehaired fox terriers, Brussels griffons, bichon frises, Australian terriers, Manchester terriers and basenjis.
Kerry blue terriers are medium-sized dogs with soft, curly coats that don't molt. While they might not shed on their own, you'll need to groom them regularly or their coats will become matted and full of dead hair. If you're looking for a low-shedding dog of a medium size, you could also consider a Tibetan terrier, whippet, Portuguese water dog, Lakeland terrier, Irish terrier, standard schnauzer or puli.
If you love big, shaggy dogs, but don't like them shedding everywhere, you might be interested in a Spanish water dog or a Bouvier des Flandres. Like many other low-shedding dogs, they still lose hair, but it doesn't easily drop out on its own, so you will need to help them out by brushing them a few times a week. Other large, low-shedding dogs include standard poodles, Airedale terriers, salukis, wirehaired pointing griffons and komondors.