My favorite way to store fabric is in drawers, folded to the width of the drawer and then filed as one does folders. For smaller pieces, use smaller drawers and wrap fabric around pieces of cardstock or chipboard to provide stability.
Check out these fabric storage and organization tips from around the web:
Everything Etsy – Part One and Part Two
Sew We Quilt
Operation: Sewing Room Organization Flickr Group
Cut to Pieces
How do you store your fabric?