Most people with Asthma can exercise and become fit. But the type, and intensity of exercise Asthmatics can do varies greatly from person to person. Here's a video that outlines the rules of thumb.
Asthmatic or not, be sure to consult your doctor before beginning any exercise program. Asthma is a chronic disease of the airways. It causes bronchial passages to become inflamed and arrowed in response to triggers like cold, exercise, and stress, and allergens like dust mites, dander and smoke.