There are actually two main types of allergens in cats- dander and saliva. If you're allergic to dander, some breeds are nearly dander-free, or some individuals clean their dander religiously. I have one cat who grooms ~6 hours per day, and my family with dander allergens can sit with her on their laps without any problems. Saliva can be a bit harder to deal with, since it gets all in their fur when they groom. If you're unfortunate enough to react strongly to both allergens, you're probably SOL, but it's always worth looking in to.
I luff my kitties. They're thirteen and fourteen, and I'm going to cry like a little bitch when I have to go to college and leave them. :c So glad I'm not allergic, though.