For a quilter, scraps must be greater than 1/2" wide as seam allowances are 1/4". Some may keep 1" strips or squares. Others may think those are too little to use. Personally, I will keep a 1" strip for string quilts but I determine 1" squares to be too small to keep.
Sometimes pieces are larger and they can be cut into whatever sizes the quilter frequently uses. I use leftover blocks and pieces up to 18" square for preemie quilts which are 18" square.
Here are 3 preemie quilts I finished this morning. They were made from discarded fabric that I brought home from quilt guild. The bottom one was made from squares that someone had cut. Chances are these were leftover from other projects but there were enough for a cute little preemie quilt.