Sugar plays an important role in baking besides adding sweetness. Sugar liquifies during baking, adding moisture and tenderness. Refined sugar helps cookies spread, allowing for crisp texture.

Below is a comparison between various natural and artificial sweeteners.

Natural Sweeteners

Sweetener Baking Properties
Honey Honey is 25% to 50% as sweet as granulated sugar. Colors and flavors can vary, depending on the diet of the bees that produced it. Baked goods made with honey tend to come out denser and darker than those made with granulated sugar.

To use honey in place of granulated sugar, use 3/4 cup plus 1 tablespoon of honey and reduce liquid in the overall recipe by about 2 tablespoons. Add a pinch of baking soda to reduce acidity unless the recipe calls for buttermilk or sour cream.
Maple Syrup Maple syrup has 60% of the sweetness as granulated sugar.  This is made from the boiled-down sap of the maple sugar tree. The syrup is a combination of sucrose and glucose. Syrups come in grades, where grade A is a golden brown with a light flavor. Grade B is darker, thicker, and has a stronger flavor, which makes it suitable for baking. 

To use maple syrup instead of sugar, use 3/4 maple syrup for every cup of granulated sugar, and decrease liquid in the recipe by abou 3 tablespoons.
Molasses Molasses is a byproduct of refined sugar production. Brown sugar is made by adding this to granulated sugar. Molasses actually has a small amount of calcium, vitamin B and iron. It has a strong flavor in baked goods but is not as sweet.

When substituting, use 1 1/3 cups molasses for 1 cup sugar, and reduce the amount of liquid in the recipe by 5 tablespoons. Since molasses is acidic, add 1/2 teaspoon of baking soda to each cup of molasses used. Be sure to replace no more than half the sugar in the recipe with molasses.
Corn Syrup Corn syrup is not as sweet as sugar and does not add flavor to recipes like honey or molasses. It is made by treating corn with enzymes to break down its starch into maltose and glucose. It does not crystallize and is therefore useful in candy making. Golden Syrup is used in the United Kingdom in place of corn syrup. Some believe it adds more character to certain dishes than corn syrup.

Artificial Sweeteners

Sweetener Baking Properties
Sucralose Sold under the brand name Splenda®, it is a sweetener made from sugar but not metabolized by the body like sugar. It is 66 times sweeter than granulated sugar. Recipes made from this product tend to bake faster than usual, so be sure to check for doneness more frequently than the recipe calls for.

To substitute, use 1 cup of sucralose for each cup of granulated sugar.
Aspartame This is 160 to 220 times sweeter than sugar, however it loses its sweetening power when heated.  It therefore cannot be used for cakes or cookies. It can be used in no-bake puddings and pies after removed from heat.

Six (1 gram) packets can be substituted for each 1/4 cup of sugar. 

This is sold under the brand names of NutraSweet® and Equal®.
Saccharine  Anywhere from 200 to 700 times sweeter than sugar, saccharine is usually sold under the brand name of Sweet and Low®. It is recommended to substitute it for only half of the sugar in a recipe.

You can use six (1 gram) packets of it for 1/4 cup of sugar.
Acesuflame Potassium This is sold under the brand names of Sweet One® and Sunette®. This can be used in combination with sugar when baking.

Use six (1 gram) packets of acesuflame potassium for each 1/4 cup of granulated sugar.

The substitutions mentioned here are just guidelines. Sweeten to taste as you would season to taste with salt or pepper.