I serge the edges of all my quilts before I bind them. I also serge the edges of the binding before I sew it on - it stabilizes the binding so that the top layer doesn't shift away as you are sewing and the serged seams help fill the binding and make it "stuffed."
I made a whole quilt with a serger once - a snowball quilt for my new granddaughter. The back of that quilt was the prettiest quilt back I'd ever seen.
I serge the edges of quilt labels, press them under and applique them to the quilt.
I serge scraps of muslin into 2-3" rectangles and keep them in a bag with small safety pins. When I cut fabric from a large piece of yardage or batting, I write the size of what's left on the scrap and pin it to the leftover. The next time I'm looking for a backing fabric or piece of batting for a small quilt, I can just look at the tags to find a piece that's big enough without having to measure every one of them, again. When I cut more off, I draw a line through the old measurement and write the new measurement underneath.