Flax is by far my favorite egg substitute. It's quick, easy, and doesn't require anything that includes corn or starch. In comparison to bananas or other egg replacers, flax meal + water will yield a light, fluffy texture to most baked goods.
To implement:
Using a Vitamix, or other powerful blender, obliterate some flax seeds. If you already have flax meal, make sure it hasn't gone rancid. Fresh flax meal is best.
For every 1 egg a recipe requires, mix 1 tablespoon of flax in 2.5 tablespoons of water. Most resources will say to use 3 tablespoons of water, but this might throw off the ratio of liquid to solids a recipe requires. I've found that, thinking in terms of eggs, 2.5 tablespoons of water is equivalent to the liquid most eggs contain.
Let the flax and water soak into each other for about 10-20 minutes before mixing it into whatever you're making. That was easy!