Portuguese water dog
Portuguese water dogs don't require a lot of grooming because they don't shed that much, making them great for people with allergies. President Barack Obama has one for that reason!
Furless cats or dogs
Pets with less fur don't have dander and are less likely to bring in the allergens from outside that cause you just as much trouble. Try a sphynx cat or Mexican hairless dog, but beware. These little guys need just as much care. They need regular moisturizing and have to be protected from the sun.
Reptiles & amphibians
They may be scaly or look slimy, but amphibians and reptiles have a lot of personality, making them fun pets for everyone. But some, like turtles, can carry salmonella, so consider it carefully and do your research if you have little ones in the house.
If you're committed to something fuzzy, hamsters, gerbils and other rodents are a good option. If you're extra sensitive, make sure you handle one for a little while before committing. They do have dander, but they're very small (so there's less of it) and they stay confined to a cage most of the time.
Devon rex cat
If your feline allergy is mild, try a Devon rex. They do have dander, but have less fur than many other breeds, meaning they lick themselves less frequently. Since some proteins in cat saliva cause allergic reactions in some people, those with mild to moderate allergies may be able to tolerate this less furry kitty.
Kerry blue terrier
With less dander than other breeds, the Kerry blue terrier has a soft, wavy coat that allergy sufferers can actually touch. If you've already got one of the cats mentioned above, though, steer clear. Because of this breed's hunting instincts, he may terrorize Mittens.
Standard poodle, American labradoodle or bichon frise
Standard poodles have a long hair-growth cycle (that they've passed on to their crossbred cousin, the labradoodle). Because of this, they typically shed less. Also, the standard poodle's curly hair tends to retain the dander, rather than let it loose in the air. Similarly, the bichon frise will retain most of her dander until washing. All of these dogs, however, often require professional grooming.
At the end of the day, fish really are the only truly hypoallergenic pet. They're confined to a small, watery environment that isn't likely to be full of the allergens other pets can leave around your home.
How to choose
Before you buy a pet, it's best to fully research everything from their typical personality traits to their eating and grooming needs. A labradoodle is a large dog and will require much more food than a sphynx cat, which can get pretty pricey. Grooming can also be pricey and many dog breeds, especially larger ones, have potentially expensive common health issues, which means racking up a pretty hefty vet bill at times.
You should also ask your allergist or general practitioner about the real cause of your allergies. Are you allergic to dander from the pet or is your long-haired love just bringing in plenty of pollen to make you sneeze? Take your time and don't rush into it.
More on pet allergies