I don't throw stuff away. I even save the ends of binding.
It all ends up in this basket.
Once when I was feeling REALLY organized, I matched up colors and stitched them together and even marked the length. That only happened once, it was a few years ago and I'm over it.
I did have 230" of scrappy blue binding for this quilt. After I got it sewed on, I had 4" left. That went into my strings bin which is another (ok, several) overflowing bucket.
The scrappy binding looks great on my scrappy quilt!