I don't have old belts but I do have a belt display case that I'm quite proud of (Ikea Kasseby box). I wear an A2 belt normally. The white belt in it is the A4 I bought for when I was pregnant.

I gave all my past belts to other students when they were promoted to the respective belt. In my view, this created some kind of bond with the rest of the team. Luckly, I took pictures and competed in every belt division I passed by.

I don't see seem to get attached to my belts, like at all... have hard time imagining keeping my old ones. Some have been nicer than others but it's been only for the functionality or the look. I even wash mine for chrissakes! :D (Maybe that's why I'm not any better.) I have had more affinity towards some gis, and been sad when they've finally broken enough so I had to retire them. Perhaps things will be different if I ever get a black black belt & manage to not lose it for 3+ years. :) Also those custom displays are pretty awesome!