I use YLI Silk Thread for all of my applique work. I like it because the stitches literally disappear in the fabric. I've been using it for several years now and have not had any of my applique come apart. And my quilts do get used and washed.
I got the YLI at a local quilt shop but you can find it online at Red Rock Threads. In fact I think they have two or three brands for silk thread.