Though I am no longer a strict vegan, I continue to use egg substitutes in some of my baking. However, these days I prefer to go the less processed route and often use flax seeds instead of eggs or Egg Replacer.
More discussion on these substitutes, plus others, below the jump…
• Energ-G Egg Replacer – Made from potato and tapioca starch, Egg Replacer is free of eggs, gluten, wheat, casein, dairy, yeast, soy, tree nuts, and peanuts, making it useful for vegans and those with food allergies. Mixed with water, this relatively flavorless product does a good job of mimicking eggs in baked goods like cookies, muffins, and some cakes. The ratios on the box are a good starting point but depending on your recipe, you may have to play around a bit.
• Flaxseed – Finely ground flax makes an excellent binder; however, it has a nutty flavor that's best reserved for whole grain baked goods and pancakes. (Sara Kate did use flax in her Vegan/Gluten-Free Chocolate Cupcakes, with good results.) For more discussion and ratios, see this post.
• Silken tofu – Silken tofu is relatively flavorless but it can make baked goods dense, so it's best used in brownies and some quick breads and cakes. Use 1/4 cup of pureed tofu for 1 egg.
• Baking soda and vinegar – This is a decent egg substitute for fluffier baked goods. Use 1 teaspoon of baking soda mixed with 1 tablespoon of white vinegar for 1 egg.
• Banana – Different sources recommend anywhere from 1/2 to 1 mashed banana as a replacement for 1 egg in muffins and cakes. I haven't actually used this one as I'm allergic to banana, but I'm sure some readers can chime in!
Do you bake without eggs? Share your own tips and experiences in the comments.