Yeah, I threw away a lot of the boxes too. My older brother is the only reason I have any of the boxes from the NES and SNES era. He managed to save his SNES box, though no styrofoam, a Starfox box, and that Dragon Warrior NES box. The rest of my boxed stuff is things I got later on when I started collecting.
I wish that I had kept the boxes, but most of them were at Christmas or Birthdays, so they probably go trashed fairly quickly. I am glad that the Genesis games came in those hard plastic shells.