Though the primary purpose of sugar is to add sweetness to foods, it's also useful for the way it behaves chemically in recipes. Sugar is what makes whipped eggs and butter fluffy, as well as what gives baked goods that tasty-looking, golden brown color. The type of sweetness you want to add is going to vary, which makes it a good idea to have a few different types of sugar stashed in the cupboards. Granulated and powdered sugars are staples you'll want to stock, but corn syrup is another sweetener you might want to keep around. Corn syrup gets a lot of bad press for its inclusion in processed foods, but used in moderation, it can extend the shelf life of baked goods -- which is especially helpful if you plan on making big batches of holiday treats well in advance of the season.
Brown sugar is instrumental in many recipes, but unless baking with it is something you do on a regular basis, it might be better to buy it in small quantities. Brown sugar clumps much faster than regular sugar, and it will turn rock-hard quickly when left on the shelf, especially if not stored in an airtight container.
Reducing the calorie count with artificial sweeteners is a big no in baking. Whether or not you can tell the difference in flavor, they never make an effective substitute. Artificial sweeteners don't undergo the same chemical changes during baking that sugar does, so your cakes and cookies might not turn out as fluffy or golden brown as you'd hoped.