Whether you are out of eggs, are vegan, or for any other reason, it is always nice to be able to substitute an egg in baking when necessary. The substitution below applies to baked goods such as muffins, loafs, cookies, and cakes, but does not apply to recipes where eggs are the primary ingredient, for example frittatas, crêpes, or soufflés.
The perfect substitution for eggs in baking is for every 1 egg, use a mixture of 1 tablespoons of ground flax seed and 3 tablespoons of room temperature water. The only warning I wish to impart is that substituting for more than 2 eggs in baking does not yield the most favourable results, at least in my experience.
1 egg = 3 tablespoons of water + 1 tablespoons of ground flax seed