Yes, Patty, I do stabilize.
When doing custom I will do the "bones" of the quilt first - SID between the borders and around the blocks before doing any of the fill work. This helps you keep the individual elements of the quilt - and the entire quilt itself - square and straight. Then I go back and do the designs or fill work.
In the areas I am NOT quilting, I will baste - either with pins or a large basting stitch, until I go back and do the fill work in them to keep them from shifting or puckering.