There's a product called Ener-G Egg Replacer and works perfectly for baking and baking only. Obviously it doesn't work for making things tasty "eggy" like in an egg bagel or challah, but it'll work for any other baked good without issue.

I use it in my vegan baking all the time. With the price of eggs, I've been using it in lieu of eggs in my non vegan baked goods too.