Yep, stitch the pieces down if it will be washed. If it's a wallhanging and won't be washed, then I would still do some stitching on each piece but it doesn't have to be around the edges. For a quilt to be washed, I would stitch around the edges in a style that compliments the quilt. For realistic animal applique, I'm with Wendy - stitch around the outside edge with a simple straight stitch. I often will save the stitching to do while quilting since I generally want to quilt around the edges of the applique anyway. That saves some time since then I'm only stitching once instead of twice. But it also puts the quilting slightly inside of the applique rather than slightly outside of it, so you'll have to decide if you like that. One word of warning with that straight stitch on the edge is that you need to be careful about how close to the edge you get. If you get too close, you'll cause fraying. So you want to get as close as possible without getting too close. That just takes a little practice and will be different depending on the type of fabric used for the applique.
Nancy