I don't have a hard and fast rule, but if I can't wrap it around my comic boards, then it goes into the bin with usable scraps. It probably has to be 2 1/2" - 3" for me to keep as a "usable scrap", but if it's a long 2" scrap, I would keep that, too, since that makes it more likely I would use it for something.
Anything smaller I put into a separate pail which theoretically I can use for stuffing - I just starting doing that maybe six months ago and haven't made anything needing stuffing since then, but I have occasionally pulled something out of the pail when I want a really small piece for something.
I'm still trying to achieve a balance. I don't like to feel like I'm wasting things, but if I save too much, the organization becomes overwhelming.