I have a ridiculous amount of ribbon and have organized it a hundred different ways. This has been my most successful attempt. I utilize an Ikea kitchen island as a desk and it has a shelf underneath the drawers. I need my ribbon to be handy, I need to find it quickly without hours of searching, I need to keep it clean, and I don't want to see it. I bought these lined baskets on sale from Michaels, then stored ribbon in sandwich sized plastic bags, and stood them up inside each basket, arranged by color.
For the ribbons themselves, I either wind small amounts in finger eights and utilize the ties that come with my boxes of garbage bags (string could work just as well), leave it on the roll, or cut it from trim cards. The key for me is that the ribbon is in smaller bags, meaning I can easily grab a bag and see what's in there without having to rummage around in it. It saves me a lot of time. Granted, most people don't have this amount of ribbon to contend with, but....