I finally got a brilliant idea... game storage containers! Since I'm cheap and didn't want to spend money, I decided to make my own instead.
Materials: A standard elementary school ruler, a razor blade, pencil, duct tape & the old cardboard box I was storing all the games in.
I measured each type of game cartridge, traced out the dimensions on pieces of cardboard, cut them out, taped the ends, and.... Success!
For the game cartridges that I didn't have too many of, I simply slipped a rubber band around the cardboard container to act as a holder so the games stayed up neatly. Worked like a charm.
So now the game room stays clean for a total cost of... Free.