I have 3 big flat plastic storage containers under my desk, which I am allowed to access only when the resident large ginger "guardian of the ribbon" is not in residence! The top one is for ribbon and the other 2 for card/paper scraps (solid colors in one, patterned in the other).
He would prefer me to leave the lid off the container so that he could actually sleep ON the ribbon, but that's not going to happen.
I roll my ribbon and wrap a piece of scrap paper around it (just like Bonnie does here at Really Reasonable Ribbon), then store it by color in clear ziplock bags. Any smaller scraps (8"-12" or less) are gathered and stuck onto a safety pin, like this
and stored in the relevant bag as well. It's amazing how often I only need a few inches of ribbon for a project, and my first port of call is always the safety pin scraps before I go cutting any off the longer pieces. Waste not, want not, my grandmother always said!
It's easy to just reach under my desk and grab the ribbon bag in the color I'm working with, and match up something suitable by looking through the plastic, rather than taking the whole lot out of the bag.
If there are any multicolored ribbons that don't have a distinctive color theme, then they go into a separate "multi" bag. Black and white are stored together.
And that's it folks! It may not be sophisticated, but I like it and it works for me. I'm sure you'll have lots of wonderful storage ideas to choose from when the organization week is over, and don't forget to enter the draws for the great prizes on offer.