Some good substitutes that can be used in baking in place of eggs are cooked pumpkin, tofu, applesauce, yogurt, buttermilk, or cornstarch solution. Other alternatives are gelatin, a solution of ground flax seeds and water, vegetable oil or a solution made of soy flour and water.
Using any of these substitutes in place of eggs may give baked goods a taste and texture differing from the usual. Also, the various substitutes correspond best with different baked goods. Yogurt, applesauce and flax seed solution are very effective egg substitutes when baking brownies, while buttermilk, gelatin and soy flour solution work best as substitutes when baking cakes.
Additionally, the egg substitutes have to be used in correct proportions to be most effective. For example, 1 egg is 1/4 cup blended tofu, 1/3 cup applesauce, 1/4 cup yogurt, or 1/4 cup vegetable oil.