If you realize too late that your eggs didn't make it into the batter, don't stress out too much -- leaving eggs out of a typical baking mix typically won't ruin the final product. Eggs serve multiple purposes in a baked good, from binding the ingredients to helping it rise. Luckily, other ingredients in your mix perform some of the same functions, and can help pick up the slack when you find yourself eggless.
The Purpose of Eggs in Baking
Eggs are used in baking for a few reasons. They bind ingredients together; they help the batter rise while it's baking; and they make your baked goods moist and chewy. Fortunately, eggs are only one of a few ingredients that perform these functions in a standard baking mix.
Binding Baked Goods
The main ingredient in most cakes or cookies is flour. Gluten, the protein found in flour, is a good binding agent itself. Without eggs, goods baked with flour or a standard baking mix will be a little more delicate, so you might consider leaving a cake in the pan instead of turning it out to serve it. Another trick is to freeze the entire cake or loaf, then run a knife along the rim and heat the bottom over a flame on the stove. The cake should pop out in one piece. Goods baked with gluten-free mixes or flour won't bind at all without eggs or an egg substitute.
Leavening the Mix
Eggs do contribute somewhat to leavening in a baking mix, especially if the whites are whipped first. Baking powder or baking soda mixed with vinegar or lemon juice are also common leaveners in a baking mix, and are already part of any boxed mix. As long as you didn't forget the baking powder as well, or if you're using a box mix, your dessert should rise just fine. It might be a tiny bit flatter than usual, but it won't be terribly noticeable.
Making It Moist
Eggs help to make your baked goods moist, though oil or butter in a recipe also serve the same purpose. Skipping eggs is more noticeable in cookies than in cakes or breads. Eggless cookies tend to turn out flatter and crispier, but sometimes this is even done on purpose.