Baking without eggs can be tricky but it can be done. Eggs provide liquid in the recipe, so if you leave eggs out you need to replace them with something else.
Powdered egg replacer: This stuff is great. This is what I use most of the time. It is available at health food stores but even grocery stores carry it now. It may seem pricey at 4-5.00 a box, but one box last for months.
Banana: Use 1/2 a banana, mashed to replace one egg in sweet baked goods.
Applesauce: Add about 1/4 cup applesauce in place of an egg in sweet baked goods. It's a great binder but you may need to add a little extra baking powder (about 1/2 tsp) to help with the rising.
Tofu: Use about 1/4 cup mashed silken tofu for one egg. Also add 1/4-1/2 tsp extra baking powder.
Soy flour: Use 1 heaping tbsp of soy flour or cornstarch plus 2 tbsp water to repace each egg in a recipe.
-The Garden of Vegan