If I don't have eggs, but I'm in the middle of baking I use this simple egg substitute recipe:
1 egg = 2 t water + 1t oil + 2 t. baking powder
I have used it for cakes, brownie mixes, pancakes, cookies. And only recipes that use eggs as a leavening agent but not for binding. Its a quick and easy fix.
I did google this earlier and found this helpful website if you'd like more information: