If it is smaller than my hand it goes in the scrap bin and I keep bits right down to about an inch. I love to do applique with my embroidery machine and its amazing how often the perfect colour was that tiny piece that got chopped off an edge of something or was left from a go cutter fold.
I keep fat quarters and eighths sort of sized pieces in a bin together. Everything else gets folded and sorted by colour in the stash.
I was also keeping the scniblets to add to a pet bed but I thought it felt kind of lumpy and she's getting older and likes her memory foam mattress with a quilt gone wrong cover so they went to the garbage. Space is valuable too.