There are plenty of people who love dogs, but suffer from allergies. For them, a dream dog is any dog that does not cause them to have an allergic reaction. Unfortunately, no such dog exists. But there are some dog breeds which are known to have an increased chance of success when it comes to being hypoallergenic - meaning that they are relatively unlikely to cause an allergic reaction.
One of the first things to realize about allergens and dogs, is that the allergen is not the dog's fur or hair, but rather it is the protein found in the dog's saliva or in their dander (dead skin cells).
There are many thoughts about hypoallergenic dogs, all of which hold some truth for some people. One theory is that small dogs produce less dander because of their size alone. Another is that low shedding dogs are more hypoallergenic because there is less loose dog hair around for the dander to stick to. But dog hair clumps on the floor and furniture, whereas dead skin cells tend to be more airborne.
Generalizations can be made about a breed, but each individual dog is different, just like each individual's allergies are different. The key is to work with different breeders in finding the right dog for you. A good breeder will allow you to try a puppy on a trial basis, and will take him back if he does not work out. If you are determined to have a dog as a pet, it may take a few tries to find a dog that will work for you, but you will discover that it is worth it.
Remember, you can cut down on dog dander by bathing your dog regularly (about once a week), keeping your home clean (vacuum and dust regularly), by not allowing the dog in areas of the house where the allergy sufferer spends the most time (especially their bedroom), and by allowing the dog to spend time outdoors.
The list below are of dogs that produce less dander than other breeds. The ones with asterisks (*) are breeds recommended by the AKC for allergy sufferers to try. The others are dog breeds that have been recommended from other sources, or that are non-AKC breeds.