Eggs as a Binder* substitutions for one egg include:
1/2 of a medium banana, mashed
1/4 cup of applesauce (or other pureed fruit)
1 tablespoon ground flax seed mixed with 3 tablespoons warm water; let stand 1 minute before using

Eggs as a Leavening Agent
1-1/2 tablespoons vegetable oil mixed with 1-1/2 tablespoons water and 1 teaspoon baking POWDER (not soda) per egg.
*http://www.kidswithfoodallergies.org/resourcespre.php?id=104#egg-substitutes-in-baking


Peta's excellent suggestions**

1 egg = 2 Tbsp. potato starch
1 egg = 1/4 cup mashed potatoes
1 egg = 1/4 cup canned pumpkin or squash
1 egg = 1/4 cup puréed prunes
1 egg = 2 Tbsp. water + 1 Tbsp. oil + 2 tsp. baking powder
1 egg = 1 Tbsp. ground flax seed simmered in 3 Tbsp. water
1 egg white = 1 Tbsp. plain agar powder dissolved in 1 Tbsp. water, whipped, chilled, and whipped again

**http://www.peta.org/living/food/egg-replacements/


Substitute for eggs to use in an omelette type of dish

As a binder in vegan loafs and cookies, I use ground flaxseed

The binding effect of egg in baking can be substituted by using ground flaxseed. Ground flaxseed can be found at most supermarkets. Ask you grocer to stock it. Here's a picture of ground flaxseed from WholeFoods. You can also find it at many pharmacies and at Walmart. It's sold in the vitamin department. Ask for ground flaxseeds. Flaxseed is often sold organic and that is about 3 times more expensive than non-organic. I use non-organic 

1 egg = 1 tb ground flaxseed with 3 tb warm water.

    2 tb gives 3 grams of protein -->