I'll always keep product boxes for the more valuable stuff, more for storing/moving than selling (though that's always an option). And if they came in a shipper box I'd probably keep those too since they wouldn't take up much more room. Reckon when I get enough boxes, I'll just seal them in the shippers, stuff them inside another box or container and put 'em in the shed for storage.
I've thrown out the boxes of the lesser toys, though - stuff I'll never sell, isn't worth a great deal, or isn't particularly fragile.