Lets see, I was one of the best sprinters in my school.
I regularly sailed small craft (the hardest kind), kyaked, cycled(miles), I was a competitive swimmer, climbed mountains (both hiking and literal rock climbing), and played a whole host of competitive sports (football, rugby, baseball doesn't really count...), was considered a wunderkind at Tae Kwon Do
All with asthma, and was damn good at some of them (read; nationally competitive). Just endurance **** didn't work for me (despite some of those activities if you paced yourself correctly I'd never feel the asthma), though my muscle type is also not really tuned for endurance, my strength and speed is well above the norm, but between asthma and my muscle type - I could probably never ever run a marathon.