I've still got the boxes for some of our really old games (Battletech Crescent Hawks revenge, Wingcommander 1 etc), but got rid of most of the boxes years ago for space reasons, generally only keeping the boxes that I really liked
Hangtime, I think part of the reason they kept the boxes as long as they did was because for a very long time they needed them for the floppies and manuals
IIRC once they stopped doing floppy versions the boxes started to get a little smaller, and once they stopped doing proper manuals the boxes started to shift down to size, although it wasn't really until DVD cases became available that they really killed them off (I guess DVD cases were/are more durable than CD cases on shelves, and had room for a manual).
I actually found a load of old Snes and Gameboy boxes in the loft the other day, which i think i'll have to dispose of, as AFAIK most of the games went down to my nephews a few years back and have disappeared
(I've still got the snes's etc just no games these days).