Dogs that don't shed do exist! These breeds have nearly-hypoallergenic coats producing less dander, the main allergen in humans.
Afghan Hounds are independent, loyal, and require regular grooming. Their long, silky coats don't shed but need maintenance.
Bedlington Terriers have a unique, lamb-like coat. They require little grooming and their coat is low-allergen.
Bichon Frise, resembling miniature Poodles, have low-allergen coats. Their hair grows continually but doesn't shed.
Chinese Crested dogs are mostly hairless, making grooming easy. Their skin needs protection in extreme temperatures.
Kerry Blue Terriers are people-oriented and intelligent. Their soft, dense, low-allergen coats need regular grooming.
Poodles, in all sizes, have a soft, hypoallergenic coat of curly hair. They shed minimally and require regular brushing.