Baking without eggs is one of the trickiest things I have encountered in the kitchen . . . that and those darn macarons! 

I have tried many different subs for eggs- applesauce, bananas, oil- but I have found the most success with the powdered egg substitute that I found in the Gluten Free area of my grocery store.  The powder is made of potato starch, baking powder and corn starch.

 Good luck in your egg-less endeavors!! Let me know in the comment section if you have had success with a certain egg substitution, as I would love to know what works for you.