Not to want to contradict people, as yes cat fur does cause allergies, but this is more common with asthematics.
People who are not asthematic and allergic to cats are very often allergic to something in the saliver. As a cat cleans themselves it obviously gets on the fur that way too.

Okay some tips:
As already said, keep the cat away from the bedrooms, when I was younger, my dad would not allow my cats in the upstairs of the house, cats lern rules pretty fast and so correct discipline, these cats will know their boundaries.

Keep the cats of the furniture, sofa etc, don't worry, cats are perfectly comfortable on the floor.

When the cat is old enough, allow it outside (obviously a bit of a problem if its a pedigree).

Possibilty of bathing the cat should clean the saliver and the allergen off of the cat.

Girls are better than boys for producing less of the allergen, something to do with testosterone (and have you seen how much the boys drool when they are happy!)

And of course hoover the house and wash the cats bedding frequently.


Ah-ha I have found a brilliant link:
HELP - I'M ALLERGIC TO THE CAT