The latest catalogue of Doctor House DK proposes a few clever ways to store ribbons. The first idea is to install a metal wall hook on a door. The key is to make sure that the hooks are long enough. You could reproduce the look and feel with long nails on a piece of wood.
Another solution is to neatly place them on a basket. The advantage of a wire basket over a solid one is that you can find more easily a ribbon suitable for your project.
Lastly, you could use a wall wooden bookcase or a wall. The rustic feel will add charm to your display. When you get tired to see a ribbon, you can always repurpose it as a candle holder.
Finally, you could use metal pails as shown on the blog of Candice Stringham photography. Her solution works best with thin ribbon rolls.