I only save it if it is 1.5" or wider. Maybe someday I'll try making a rag rug, or something using the clothesline and scraps, but I'll continue to produce those. In the meantime, there is therapy in cleaning up a mess and throwing it away. I'm constantly creating more messes, and in order to create a measure of order, I need to throw away the tiny stuff.
If someone does think of some real use for the small pieces of batting, please let me know as I have a couple of bags of it (by small, I mean, smaller than what I would use for a rag quilt--so smaller than about 6" square.) I'm not interested in making pin cushions. Most people I know don't sew and I have a magnetic pin cushion that I like so I don't need any.