Maybe this is well-known to vegans and those with egg allergies, but it's news to me. I recently read on a package of flaxseed meal that it can be used as an egg replacement in some recipes. Here in a Hindu society, eggless recipes are a must. Alongside the regular Duncan Hines and Betty Crocker cakes mixes on the grocery store shelves, you'll see eggless varieties.
I tried the flaxseed replacement with a loaf of bread. A risky move, given the delicate balance of bread ingredients. For each egg I mixed 1 tablespoon of flaxseed meal with 3 tablespoons of water. I let it sit for a couple minutes to thicken up, then I added it to my bread at the time when I would have added the eggs. It worked! I never would have known there wasn't egg in the dough. I didn't notice any change in the taste or texture of the bread at all.
I think this could work well for a variety of baked goods. I'm surprised that news of this flaxseed replacement hasn't hit the bakeries here yet. Flaxseed is difficult to find, but I do see it occasionally in grocery stores. If more people knew about it, maybe there would be more flaxseed on the shelves.