There's a product called Ener-G Egg Replacer and I use it to great success for eggs in dough. It won't make a dough "eggy" like is needed for challah or egg bagels, but it'll work as a binder in other baking recipes, as far as I can tell, perfectly. I've never had anyone ask "did you do something different here?" when tasting my baked goods, even if they've had my egged versions previously.

I used to use it just for making food for my vegan pals but now I've just been using it whenever eggs are called for.