Here is some information from the UK Kennel Club:

Studies have shown that dog hair can induce asthma attacks and other related respiratory problems, as well as certain allergies and, indeed the advice received from The Asthma Research Council is that it is probably better not to have a dog at all.

However, it is understood that this is not an option for some people and therefore, it would be better to opt for a breed of dog, which does not moult. The following is a list of supposedly non moulting breeds and, for further advice on their characteristics, coat etc., advise the customer to contact the relevant Breed Club Secretaries who should be able to give expert advice on that particular breed.

BEDLINGTON TERRIER
POODLE
FOX TERRIER (WIRE)
YORKSHIRE TERRIER
PORTUGUESE WATER DOG
BICHON FRISE
MALTESE
AFGHAN HOUND
KERRY BLUE TERRIER
TIBETAN TERRIER