For me it depends on the box. I think the Halo Reach Legendary packaging is pretty nifty, so I've kept it. The flimsy Black Ops Prestige box, on the other hand, held little interest for me. Sure I could flatten it, but even then it wasn't worth the clutter to me.
At the same time, I have every box of every console I've owned going back to the Atari 5200. Not sure why since I'll never get rid of the consoles themselves, but at least the boxes are good for storing other stuff.