If you are a self-contained backpacker, your stand will be substantially different from that of a weekend or RV camper with lots of storage space and no weight limit. For backpackers, a stove is already a substantial weight commitment, so any additional weight must be carefully considered. Also remember that your stove stand does not just need to hold your stove, but rather your stove and whatever you are cooking, which can dramatically increase the weight on the stand.
Many small backpacking stoves, such as the Mountain Safety Research models, have specifically designed stands, made of lightweight aluminum. These usually provide a small, stable surface for the stove element and attach to the stove's gas bottle. These are simple, light, and usually fairly reasonable in price. A do-it-yourselfer has several other options. An upside down pie plate offers a nice, smooth surface for the stove, and weighs very little, but you will have to put something under it to support the center, because it is flimsy. A lid for a camping pot can also function nicely as a stove stand. There are other options available for purchase at camping supply stores, but since the only purpose of the stove stand is to provide a stable surface for your stove, why buy something expensive?
If you aren't hauling your own equipment a long distance on your back, you have many more options. A few milk crates held together with zip ties make an excellent camp kitchen surface, with space for your stove, your gas bottle, and other cooking paraphernalia. This design can also be expanded to support a Coleman-type two-burner camp stove, which is much bigger than a backpacking stove. A simple folding table, such as the kind made by Rubbermaid, is a good option for supporting an entire outdoor kitchen, as well as your stove. If you plan to use a campground picnic table, a simple aluminum cookie sheet will keep the hot stove off the wooden table.