Use 1/4 cup of yogurt or buttermilk in place of 1 egg while baking cakes, brownies, quick breads, cookies and flat breads. Measure yogurt in the dry measuring cup and buttermilk in the liquid measuring mug. While using yogurt I mix 3 tablespoons of yogurt with 1 tablespoon of water so that the batter is not very thick. Soy yogurt and flavored dairy yogurt can be used as well.
From various internet sources I understand that vegans can substitute buttermilk by adding 1-2 teaspoons of vinegar/lemon juice to 1 cup of soy milk and let it stand for 5 minutes. Measure 1/4 cup of this mix to substitute the eggs. (I have not tried this.)
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recipes using yogurt and buttermilk as egg substitute in baking recipes.