I use sheets a lot for backing quilts. The better quality (tighter weave) sheets make hand-quilting a lot more difficult, but I think they're great for machine quilting. If I'm going to hand-quilt, I look for 180-count or less with a looser weave.
I pre-wash in the hottest water and dry them on the highest setting to make sure they're thoroughly pre-shrunk.
They really stand up to use and repeated washing. It could be my imagination, but I think the finished quilts are a bit warmer, too.
It's always less expensive to use sheets for twin-size quilts or smaller. Beyond that, I do the math and calculate/compare the cost of using a sheet vs. regular fabric. (Why a queen sheet costs more than double when it isn't twice the size is beyond me, but that's the way it usually is.)
I suppose if I was to ever make a quilt to enter into competition (as if I'd ever get that good. LOL) I'd spend the extra money on "fancy" fabric no matter the size. Otherwise, I'd rather save the money to spend on more fabric for tops. ;-)