I alternate saving, and tossing really small scraps. I used to save small scraps from the shows I designed (usually the swatch cards for each character), and hoped to make a Victorian style crazy quilt, with a block from each show. I carried around that laundry bag of scraps for so many years, but it was never going to happen. I don’t like actually like hand stitching details, and the fabrics were all so varied, that I was never going to get them to play nicely together, and even if I did, I’d never be able to clean the quilt if needed. So I donated them to a creative re-use store in Nashville.
Since I’m mostly a quilter now (occasional Halloween costumes aside), I tend to end up with all quilting cotton scraps, which will work more nicely together. So I organize by color. Larger pieces that could be folded up and used in a project the size of a good-sized zip pouch/medium pillow (or bigger) get stored in paper crafting bins. I have a set that fits on my shelf. If they start getting full, I make something to use stuff up, or donate pieces that don’t speak to me anymore.
The smaller pieces I slice and dice into the sizes I’m most likely to use, right after I finish a project. I cut things down into 5" strips, 5" squares, 2.5" strips, and 2.5" squares. I have 5 smaller bins for these, and again, that’s the limit. If they get full, I make something. Or I put together kits to make things at classes I teach, and sometimes include the ugly scraps to make small “quilt sandwiches” for students to practice stitching on. (Also a good way to use up scraps of quilt batting.)
If I don’t love a fabric, I toss the tinier than 2.5" bits. If I really love it, I add it to a single small bin I refer to as “Scrippy-Scraps”. They get turned into crumb-piecing blocks. Sometimes I like crumb piecing, sometimes I hate it. Right now I’m trying to do some by color, to help empty the Scrippy Scrap bin. I have a few larger chunks in pink and yellow pieced to turn into tote bags soon. In the past I’ve used chunks of crumb piecing on things like my Scrappy Paper Pieced Rainbow Star Quilted Basket