Always! If there is not box, I feel something is wrong. I keep all my accessories in their original boxes but never the purses, just because it is too awkward.
However, storing the unused boxes at home is a bit of a problem, since they take up so much space. And keep in mind, they are such a giveaway to unsuspecting husbands who believed the "this old purse" line we gave them.
I also never throw out the black shopping bags/white ribbon and have absolutely no use for them either.