This article is from the Vegetarianism FAQ, by firstname.lastname@example.org (Michael Traub) with numerous contributions by others.
A company called Ener-G makes a powdered egg-substitute that they
claim is a suitable replacement for eggs in cooking. It costs
about $5.00 (U.S.) for the equivalent of 9 or 10 dozen eggs, and
it contains no animal products.
2 oz of soft tofu can be blended with some water and added to
substitute for an egg to add consistency.
One Tbsp flax seeds (found in natural food stores) with 3 Tbsp
water can be blended for 2 to 3 minutes, or boiled for 10 minutes
or until desired consistency is achieved to substitute for one egg.
1/2 mashed banana
1/4 cup applesauce or pureed fruit
1 tsp. soy flour plus 1 Tbsp. water to substitute for one egg.