I keep the boxes for my metal toys, that way I can store those toys in their boxes and not worry about dropping them on a glass toy or something because I forgot what was in a pouch. It doesn't hurt that my metal stuff happened to come with fantastic packaging -- Njoy toys, Jimmyjane Little Steel, the Tantus Alumina line, etc.
All other packaging gets disposed of whenever I have a clear shot at recycling stuff without risk of anyone noticing. So basically, packaging sometimes has to wait until nobody's home on garbage day, but otherwise gets moved out as soon as possible. My goal is to keep the toy collection as compact as possible for hiding purposes. Having extra bulky packaging around isn't helpful toward that goal.