Here are a few egg substitutes that I have collected from friends and the internet. You can also use egg replacer, however many of these are full of strange chemicals so I like to avoid them. Besides, what can be better than a little extra flax in your recipes (hooray for omega 3s!).
1 tablespoon ground flaxseeds
3 tablespoons of liquid eg. water, rice milk, soy milk etc.
Whip flaxseeds with liquid until you get an egg-like consistency. If you use warm water it will become thicker and egg-like faster. This is a great universal egg substitute.
applesauce
great substitute in muffins, some sweet breads, and some cakes.
mashed bananas
good substitute with an overwhelming banana flavor.
Gluten Free, Soy Free, Vegan 
My favourite egg replacement is 1 tbsp chia seeds + 3 tbsp water, mix in a small bowl and let stand a few minutes until it forms a sticky glob. Fantastic in baking and super good for you!