I just toss all of the boxes immediately. I don't really feel any need to save them, although some are kind of cute. They just take up too much space. I know this is a contentious issue, but I don't see how you can really enjoy them without opening them up. Just my opinion.
My move is usually to toss the box on the floor for the kids to play with for a few days until it's nice and beaten up, then it goes to the trash. I have enough space headaches with all the ships.
I've customed up a few mostly wooden GH playsets the last couple Christmasses, to cover some play pattern needs (clones, droids, and rebels can make pretty much any inside/outside area a battle field... but what are all those aliens for? Hence, the bare bones Cantina that I LOVE and the barebones Jabba's Palace that's still missing a little something).
Almost unfortunately, the cardboard scenes are getting WAY better though... to the point it's a [still necessary] shame to get rid of them. The medal ceremony box, with that fold out flap, makes a really neat little scene.