After visiting a quilter who demonstrated how no scrap of fabric left her studio, I’m inspired to be the same way about my paper. So, that means coming up with a variety of different types of projects wherein I can use very tiny scraps of paper. (The quilter used her “useless” fabric scraps as stuffing for pillows). I’ve started to organize my paper by size. I figure I can use very tiny scraps in collages, most obviously. But I’m all ears if you have any other ideas!
Craftylyra's Crafting Space 
One thing you could try is piecing it all together to make a larger “sheet” from which you cut new pieces? I’ve been doing this with fabric and it’s a ton of fun.
Hmm…so like a random mosaic pattern on card stock or something like that? That’s an idea. What I have pictured there are just the larger pieces…I’m starting a bin of teeny pieces.
Yeah, “serendipity” sheets are great ways to use scraps. Adhere them anywhich way on a fullsize piece of sturdy cardstock, stamp or draw or paint over them if you want, modpodge, let it dry completely, then cut them up into postcards, backgrounds, diecuts, whatever. You get to see every last sliver of your favorite papers that way, and in unexpected combinations that may spur new ideas. Look for the phrase “serendipity squares” on card-making galleries to see some beautiful examples. (I love the ones that use bits of security envelope insides, postage, etc., too.)