The only thing that can disrupt the camber profile is heat. A lot of heat eg. 50-60°c can actually bring the resin back into a plyable state and the camber can be affected. basically dont put your board in a hot roof or car in the sun etc.
Other than that a board can in my opinion be stored on its edge or its end or laying down. I tend to stand mine on the tails, I suppose the truly uptight would (unnecessarily) rack them on their side.
For what it's worth I store all my board gear in my board bag hanging from a hook in my garage. That way it's ready to go at the start of the season! Now that I'm starting to collect extra boards they'll probably sit on their tails in the basement. Once I finish the basement I'll probably put a wall rack in of some kind so I get stoked all summer for the coming season.
I think the main theme of this thread is this: As long as you don't do anything unusual to your board (like heat the shit out of it, or use it as a storage shelf) chances are the abuse it gets on the hill is far worse than anything that could happen to it while it sits for months.