Here's how I store my key cap sets.
As stated previously, CPTBadAss turned me on to the
Amac Boxes at the container store. The smaller one (#60380) is for 10-keys and the taller one (60420) fits a full set of alphas and modifiers and includes spacebars. Often times, I'll use multiple large boxes for sets that have lots of kits.
If you start getting a lot of sets, then you'll probably want to box up your boxes. For that, I use the
Men's Shoebox, which also comes from the Container store. These stack as well.
Below are a few shots to better illustrate:
Stacked Up:
From Side:
With Lid:
Lid Off: