I use the "not full" ones from my quilting when I'm piecing. I've used the plastic and the cardboard ones. I like how thin the thread is for piecing because it helps the seams lay flatter. I toss the empties rather than save them. I tried re-winding them but it's too much of a pain. I have extra bobbins for my machines so no point in saving them really unless someone comes up with some artsy use for them. Then I would gladly save them and pass them on.
They do make cotton prewounds. They are harder to find than the poly ones, though.