Mix 1 tbsp ground flax with 3 tbsp warm water, let sit until it gels. Use in place of 1 egg. This works best in recipes that have 1-2 eggs rather than many eggs.
OR
1/2 banana = 1 egg
OR
1/3 cup of applesauce = 1 egg
OR
1/4 cup applesauce + 1 tsp baking powder = 1 egg
OR
increase oil in recipe by 1/4 cup = 1 egg (muffins, cakes and cookies)