I use applique stitch (never knew it was called that, but I watched this video, and that's exactly what I do
http://www.connectingthreads.com/tut...itch__D54.html). I do the same stitch when attaching my binding on the back of the quilt. Almost invisible, and I've never had any issues with the stitching coming out. Of course, this is only for applique where you have turned under the raw edge. Any raw edge applique is going to fray too much for this stitch to hold. I would machine stitch with a blanket stitch or zigzag in that case.