I have two 6 drawer plastic carts on wheels that tuck perfectly under my counter. I can't part with decent size scraps. I do a LOT of applique, so these come in handy. Sort by color - Red, Blue, Green, Orange, White, Purple, Pink, Novelty, Holiday and then these go together - Yellow & Gold, Black & Gray, Brown & Tan - perfect for my 12 drawers !!
I keep a basket on my cutting table for scraps too small for me because I know there are some quilters out there who like to make postage stamp quilts....I am NOT one of them, but will eventually put that basket out for someone else to use.
The drawers allow the scraps to lay flat, and it's easy to flip thru it to look for something. Once a year, I empty all the drawers into a box and put it "away" for a year. That way I don't continually use the same scraps in projects.