Danielle of the Minimoz blog used a plastic storage basket with holes so she could slip wooden dowels through the sides to hold spools. The holes even acted as a dispenser for the ribbon tails!
Plastic container with holes wide enough to hold two rows of ribbon spools
Wood dowels (measure the holes on your basket to find the correct diameter for your dowels)
Measure the long side of your basket. Cut two dowels at least two inches longer.
Push the first dowel through a hole in one end of the basket.
Start threading the ribbons on. When you get the the last one, stick the dowel through a hole on the other end of the basket.
Pull the ribbons through holes in the wide side.
Repeat with the second dowel.