No, definitely did not keep the original boxes. We (my siblings and I) kept the sleeves, for the most part (sometimes a sleeve got lost for a game), but I don't recall any major attempt to keep the boxes. The boxes were flimsy things anyway, so they probably would have gotten too damaged anyway unless we made a serious effort, which I know we didn't. I don't think we ever really stored them back in the cardboard box once we took them out. Just kept them in the sleeve that came with the game and put them in a drawer or cabinet or something together.

We did generally keep the booklets somewhere, but how many of them are still around I have no idea. At this point our SNES and NES games are pretty much all at my parent's house and I don't really know where, so chanced that even the game cartridges are in good condition are slim.