I use batting remnants for my QAYG projects. Those long strips are perfect for the borders.
In the past when I have had smaller pieces (such as 6 or 7" squares), I have donated them to my LQS. They like to get them to use in classes for practice of machine quilting.
As far as piecing larger pieces together, I have simply zigzagged them together, but I have friends who use a seam tape.