I try to cut my fabric scraps into the largest square I can get out of it, I have a box for 6.5", 5", 2.5" squares, then another box for 2.5" long strips-at least fat quarter size, and then another box of 2.5" strips of smaller lengths. anything less then 2.5" goes into my stuffing bag. I make stuffed animals for children in my area and use the scraps/trimmings for that.
Batting scraps-I'll piece together larger pieces to make little crafts but otherwise I chop them up and add them to my stuffing bag.