Sometimes eggs can simply be omitted from a baking recipe, if there are other ingredients present that are binding enough - but often something is lost. And egg-like substitutes are not an option as far as I'm concerned. Instead, I've come to love replacing eggs in recipes such as muffins and batter breads (banana, pumpkin, etc.) with a "flax egg." It's easy, cheap, vegan and super healthy - just whisk 1 tablespoon of ground flax with 3 tablespoons of water until thoroughly combined, and then let the mixture sit for a minute or two. It will form a gooey, stretchy consistency that provides the necessary binding properties to various baked goods, without impacting the flavor much if at all. If the overall taste of what you are making is mild, you may be slightly more aware of the presence of flax - it has a subdued, mild nutty quality - but to me at least, it's thoroughly enjoyable.And to boot, flax has tons of health benefits. Particularly for vegetarians and vegans, the omega fatty acids in flax seed are an important boost.If you find that ground flax is a little harsh on your GI system, try using a "chia egg" replacement with ground chia seeds instead.