If you are looking to adapt a baking recipe to suit a vegan, or if you simply are out of eggs, you can substitute a flax seed product for the eggs. First, you'll need to grind whole flax seeds into a powder that tends to be somewhat oily. The resulting flax seed meal is high in fiber and essential fatty acids. The food has a distinctive nutty taste, so it is a tasty substitute in things like muffins, oatmeal cookies and pancakes.
Flax seed has heart-healthy omega 3 fatty acids that are only digested when ground, so this is also a good way to increase the health benefits in your baked goods.
You may want to investigate other egg substitutes (like tofu) when baking recipes that aren't complemented by the nutty flax seed flavor.