I love this discussion. And I love scraps. So many great ideas here!
I keep them in a 16 cubby shoe stand under my sewing table. They are mostly sorted by color and type. (Cotton, flannel, minky, selvages etc.) It kinda looks like a box of crayons to me. Sew fun. Makes me want to use them. I don't precut. I do collage & applique, and never know what size I might need.
I also swap with other scrap lovers in my guild so that we all have a wider variety to pick from.
And, I donate some to a buddy who has a school class that uses everything- including batting in their art projects.
Even the smallest ones get used in pet beds.
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I use another shoe cubby just like this, also under the table, for often used supplies: glue, scissors, rotary blades, needles/pins, etc. Works for me.
Not a great picture, sorry. I have been using lots of them, and have added & subtracted lots of colors that don't show up here.