We have an egg allergy in my household. This is a tough allergy – eggs are in so many different things, and trying to accomodate this one has been a big adjustment.
Egg free baking has been the biggest hurdle. I have done a lot of research on egg-substitutes, what role eggs actually play in baking, and how to make successful baked goods without the eggs. Depending on what role the egg is playing will determine what you should use for a substitute. Some eggs act as binders, others as a rising agent..here ar some common substitutions that I have found and tried:
Muffins: eggs act mostly as a binding agent, as well as adding moisture. For one egg, you can substitute 1/2 banana, 1/4 cup applesauce or 1/4 cup oil/yogurt/sour cream.
Cookies: eggs serve as a binding agent, as well as adding moisture. For one egg, use 1/4 cup oil, or 1 tablespoon cornstach + 2 tablespoons of water.
Cakes: eggs are a leavening agent, as well as adding moisture, and making the cake light and fluffy. You can substitute for one egg: 1/4 cup oil/yogurt/buttermilk, 1/2 banana, 1 tablespoon vinegar + 1 tablespoon water + 1 teaspoon baking powder.
Breading: for breading (i.e. chicken, etc) I use buttermilk, or yogurt watered down instead of egg. This is a little messier, but works well.