In Baking, Sugar is a Liquid
Sugar mixes with water like lonely dogs in a parking lot, and then it holds on tight as a tick. This hydro-greediness gives cookie dough the lubrication is needs to spread more fully on the baking sheet, and then retain moisture longer in the jar. Leaving sugar out will only give you minor caloric savings (as compared with say, the butter) and just results in higher, drier disks you won't want to eat at all. According to my crude calculations, cutting sugar in half, using an average cookie recipe, will only save you about 15-20 calories per cookie. Not worth it!
Sugar Versus Protein
Whenever you bake something that's leavened, from cakes to pancakes, you're making good use of wheat proteins to create a sticky mass capable of holding bubbles while it firms into a delicious, cakey matrix.
This stickiness comes from gluten, a protein that only forms when water is around. Since sugar sequesters water, it inhibits some of the protein from forming. That's why pancakes made with no sugar can be bready and tough, while those made with sugar are tender and light.
It also explains why sugar is a preservative: it literally sucks the juice out of germs.