Allergies occur when your immune system is triggered by environmental factors such as pollen in the air or dander on a pet. The resulting reaction is usually itching or congestion. As many as three in 10 people in the U.S. experience allergic reactions to cats and dogs, and cat allergies are about twice as common as dog allergies, according to the Asthma and Allergy Foundation of America (AAFA). Veterinarians say there is no such thing as a completely hypoallergenic pet. But some cause fewer symptoms than others.