I'm a hoarder. My "stash" is mostly scraps. If it's 1 1/4" wide or bigger, I save it. I have 5 file boxes stuffed tight with the smaller scraps.
I did just start a scrap quilt that uses up my leftover binding strips. They are 2 1/4" wide. So I went through my bigger scraps and cut more to match. Then I need a lot of white on white for the background. So I got a lot of that from my bigger scraps. I'm to the point where I need to get into my smaller scraps to get enough pieces to make a lap size quilt. It's been fun playing with and using up my scraps.
Some people save the tiny clippings for dog bedding. I tried that once and thought, this is awful hard and lumpy, so I didn't think a dog would really like to sleep on it. So I threw those away.