If you're allergic to cats or dogs, you are not allergic to their fur, but to the dander found in their saliva or urine. These allergens can be transported to the skin or fur, where we touch dogs or cats most often.
Be aware of potential exposure to pets you may be allergic to. Ask ahead when visiting a friend's house so you can come prepared.
If you're an owner, try giving your pet a bath every week. This can significantly reduce the allergen count.
After touching a pet, keep your hands away from your eyes until you've had a chance to wash them.
Cats may cause more allergy problems than dogs simply because they tend to lick their fur or skin a lot, spreading the allergen onto their bodies.
Remember, even animals that don't shed can cause allergies.