Being brought up with parents who survived the depression, and were frugal on top of that, I took on their habits and save every scrap. I keep my fabrics in a glass front dining room buffet- anything fat quarter and above is folded, labeled for size, and stacked by general color in there. Smaller pieces- cut fat quarters and down to 3 inches go in under bed boxes sorted by color. Tiny pieces are in color categories in labeled shoe boxes on top, and the littlest are in boxes called "tidbits" and "strips."
That said, I enjoy little things and little experiments. For Valentines day, I just did a project making crumb fabrics in color groups, cut 5 hearts out from them and made a little wall hanging for my hubby. I love using the little pieces and making this and that - I also did the bitty squares project from QM last year, and my scraps were perfect for that.
As you develop your own quilting "fingerprint" you'll know better what to do. Until then, keep a few scraps to mess with, or send them on to someone who enjoys them.