I cut my scraps immediately after binding the quilt so I don't get a big bag of scraps...way too frightening for me! My scraps are cut into the following sizes to be used in scrap quilts:
5x5, 2.5 x 2.5, 2.5 x 4.5 and 2.5" strips.
These are commonly used sizes in scrap quilt patterns. I keep the different sizes in plastic containers, and keep one container just for baby and one just for Christmas.