I think this can be a tricky and heated subject, and I congratulate everyone for talking about it so respectfully... so far.
For me, something counts as cheating when I am keeping it from my partner, and he would be upset if he knew about it. It is something that breaks the trust of our relationship. It can be emotional or physical... if I am hiding it out of fear of his reaction, it is cheating.
If you have an open relationship, and the other person knows about your actions, I wouldn't consider it as cheating. The activities are within the pre-established boundaries of your relationship. I personally am not really one for sharing, but if it works for you, go for it.
I probably have a broader definition of "cheating" than most. For example... say the girls wanted to go see male strippers or something. If I told my partner about it before hand, and he gave me permission to go I wouldn't consider it to be cheating - but if I went without telling him, and hid it from him afterwards, it would definitely be breaking the rules of our relationship. This is because if he knew I did something like that without permission, he would be upset, and I would have damaged our trust.
In a relationship, my life is an open book. If my partner doesn't know something it is probably because it is too boring to know. But I am always where I say I am going to be, and with who I said I am going to be with. And if he was really interested in the minutia of my day, he is welcome to that information as well.
So for me, it is not necessarily the action, but the hiding, that makes it cheating.
Just my two cents.
-lily