Technically, I own 7. First time I had to reinstall I had lost the original box and so had to buy another for the code. In hindsight I probably could have gotten some help from Blizz but it was easier to just go get another. Anyways, that would put me at 2 if Blizz would help me out.
Then I began two boxing, so two active, one in lala land. Then 5 boxing, so 5/1. Then my son started bugging me to play and since I couldn't give up one of my accounts, I bought him his own, putting me at 6/1.
Guess I should get with Blizz and try to figure that one out, not that I really want to start paying for number 7, though it would help since I don't use my son's.
I've got so much work to do on my first team though, currently at 62, I don't see myself switching in other toons anytime soon.