Is it necessary to quilt around each appliqued piece before quilting the rest of the quilt? I have an appliqued quilt with a zillion little pieces, and would like to skip this step. What do you all (Southern talk) do?

Ready for a simple answer,No!They will hold if they have been stitched down,whether when attaching or quilting.

It will mainly depend on your choice of batting, how closely they reccomend you do your quilting. :D:D:D

Check out some of the very old ones, see how they have held up over the years. Last one I looked at closely was a Sunbonnet Sue, outline stitched by hand, still going after 40 or more years. and of course it's been washed many times. I think we obsess a lot about minor things. Do what feels good and right to you. It will turn out nicely.