I save mine. Every so often I make a bunch of pillowcase shapes of different sizes (using polyester or fabric I will never use in a quilt) and hang one beside my cutting table. I fill it with really small scraps. Then I sew up the end and make another cover for it and donate it to the local pet rescue place - the lady there donates them to a vet for cats and dogs. They love them, but I know that some rescue places don't want them, because I've recommended this to other quilters and some have tried it and couldn't give them away. I told the women at my quilt retreat about this and one of them came this year with a huge bag of scraps for me! I didn't really want donations, but a friend had given me a poly shower curtain he didn't use any more, so I cut it up and made 8 pet beds.
I wish I could get myself organized to cut my larger scraps into certain sizes, but so far they just go into colour-sorted shoe bins.