If you're allergic to pets, you're pretty much out of luck if you want a cat. Some cats are advertised as hypoallergenic, but hypoallergenic is a relative term. The best way to avoid cat allergies is to avoid cats. Normally, the allergen that triggers pet allergies isn't the cat's fur; rather, it's the dander that the cat sheds and the proteins in its saliva and urine. That's why a cat's coat doesn't really make a difference in whether you're allergic to it or not. The most common cat allergen is a glycoprotein called Fel d 1, which is found in the cat's sebaceous glands and saliva. There tends to be less Fel d 1 in neutered cats, and kittens have less than adult cats. It also appears that light-colored cats produce less Fel d 1 than dark cats; some breeds also have lower amounts of the glycoprotein than others. Still, even the cats that have less of the allergy-inducing protein can trigger reactions.
The cat breeds that are most commonly recommended for people with pet allergies include the hairless Sphinx and the Cornish Rex and Devon Rex cats. The Sphinx has active sebaceous glands, which means they're not as allergen-free as you'd think, even though they're hairless. The Rex cats have fine, fragile fur and shed less than some breeds, but they're not really allergen-free, either. Siberian cats have a better reputation as allergen-free, possibly because their thick coats prevent the sebum on the cat's skin from reaching you. Plus, they seem to have less Fel d 1 in their saliva than other breeds. Russian blue cats also have a good reputation as being relatively hypoallergenic.
Meanwhile, a company called Allerca practices selective breeding in order to create what they claim is the first truly hypoallergenic cats. For a while these cats were available commercially, but the company has shifted its focus and will no longer sell its "Lifestyle Pets" to regular consumers.