Oh boy. I save *everything*! I'm currently in my no-waste mode.
Over 1/4 yard I store folded up in one area. Under 1/4 yard I cut up into smaller squares or rectangles, whatever works. I store those in bins which are marked with the size. I'll use them for a crazy quilt later. Or a border.
I try to have a piece of every fabric go into the bin of scraps that are at least 2.5" wide. Those scraps I'm sewing onto adding machine tape, to be used as a border later.
Anything that could be used for an I Spy quilt gets cut up into 5" squares. I save 5 of each for myself (for quilts for nieces/nephews), and trade the rest on-line.
I cut up the leftovers from all that into 1.5" squares, to be used for a postage stamp quilt. Or to be traded on-line.
The leftovers (crumbs) from all of the above gets tossed into one of several drawers. I sew those pieces together randomly until they're big enough to cut into a 5" square, which I'll use for a scrap quilt later.
Whew!