As a meal replacement: Scrambled tofu with nutritional yeast and a little mustard.
In baking, there are a couple of good options:
1 T flaxseed meal plus 3 T water
½ banana or ¼ cup applesauce - Banana and applesauce work best as an egg replacer in recipes like pancakes, muffins and yeast-free quick breads, but they won’t help your recipe be as light and fluffy as they would with eggs. Just be sure to include a little baking soda or powder if the recipe doesn’t already call for it to help with this.
¼ cup Silken tofu replaces one egg. Blended with the liquid ingredients works best. It won’t change the flavor of your recipe, but it will increase the density. It works best in recipes like brownies and pancakes.
¼ cup of yogurt will also replace one egg. Similar to the notes on tofu, it will behave differently in different recipes.