I've used a quarter cup of applesauce as an egg substitute, but now I'm interested to try this method and see if it works even better! (cookingwithbooks.net)
I did not have orange juice on hand and used 1/2 cup of applesauce instead. (smittenkitchen.com)
EVEN HEALTHIER: Reduce the sugar, use whole wheat flour and make two substitutions: use 1/2 cup of applesauce for half the oil and replace 3/4 cup of flour with wheat germ. (foodlets.com)