I usually don't do anything, and normally I don't have any problems. However I just did a double-batted king-size quilt that I tied rather than quilting, and I really regret not doing something to the edges before I put the binding on. I had puckers, I have spots where the backing didn't get caught into the binding at all...it's a disaster and it was so much work that I've been procrastinating fixing any of it. I hate doing the binding anyway, and re-doing binding seems especially annoying!

At least it's just a quilt for myself (and I've been using it anyway, it's so cozy to sleep under!) I might decide to just chop off the binding all the way around and start over, rather than trying to remove it neatly. It's just big 12" blocks of fabric (super simple) so a little off the sides won't be too noticeable. Lesson learned, though. Next time I decide to double-batt anything (especially a king-size) I am stitching those edges down before I trim anything!

I also belong to the long zigzag stitch around the edges. I do this before I trim the edges. I do my binding by machine because I cannot do the hand-stitching, so I sew the binding to the back first, then fold it over and stitch the front down last. I'm happy with this technique. None of my quilts are for shows so I don't have to be concerned about judging.

I sew my binding on while the quilt is still on the long arm. I do a basting stitch as I quilt so the edges are together. I trim after I sew the binding on as I remove it from the frame.

Since I apply my binding to the front of the sandwich while it is still on the longarm, the edges are zig zag stitched keeping within a 1/4 inch from outside edge. I do the zig zag stitch along the edges as I am quilting as it helps to keep everything straight while I quilt.

I surged around one quilt and it worked beautifully. The next one was a disaster.
Now I trim back the backing to a little less than an inch from the edge of the quilt top, sew on the binding (using the magic triangle), and trim the batt and back to 3/8ths of an inch from the sewing line. I use a ruler and rotary cutter to do that in six or eight inch segments. It doesn't take that long to go around a quilt. Then I fold the binding to the back , trimming a little out of the corners and pinning the corners well, and stitch-in-the-ditch from the front.

Sometimes I find that the back folds back on itself, so perhaps a very large zig-zag would take care of that.

I use to stay stitch around my quilts.
Now I just sew the binding on the back and machine sew on the front. I am making quilts for charity (mostly young kids). I trim my quilts after they are quilted. I cut bindings 2-1/2 - 2-3/4" wide. Sometimes I sew them on with a 3/8" seam.