Most people allergic to dogs are allergic not to dogs themselves, or their fur, but to the dog's dander or saliva. Fur can harbor other allergens, like pollen and dust, that trigger allergies, though. Generally speaking, some dog breeds are worse for people with allergies than others.
Saint Bernards, hounds and bulldogs are known for excessive drooling. If you're allergic to dog saliva, avoid these breeds. German shepherds, Irish setters and English springer spaniels have lots of hair, which means more dander is produced and released into the air. Such dogs require regular baths and brushing, which allergic people should avoid.
Some dogs are prone to allergies, like Boston terriers, Shih Tzus and Lhasa apsos, which means they may suffer dry skin, itchiness, watery eyes and extra mucous output; these allergy symptoms may stir up your own allergies. West Highland white terriers are prone to seborrhea, which causes their skin to renew quickly, increasing the dander produced. Dog breeds like the Pekingese and pug have skin folds that require regular care and produce dander.
Avoid dogs who require frequent grooming, have double coats, are prone to allergies, have skin folds, are known droolers or produce excess dander.