As paranoid as I am about my stuff getting damaged, I can't imagine keeping my figures in their boxes. It seems to me that they're meant to be seen, posed, etc, so I ought to take them out. (Besides, it can't be much fun to stay in a box all day
) As careful as I am about displaying them, you really wouldn't be able to tell that they've been out of their boxes anyway (even the figmas / frauleins, which get fiddled with fairly regularly).
I keep the boxes and the plastic, though, just in case I ever need to pack them up (like if I move or something). Of course, I am beginning to run out of places to put the figures and the boxes.