The other day I tasted some egg-less brownies that a friend made with diet coke. They were very cake-like but with some chewiness. We had a Sprite on hand so we decided to try it out. All you need is 2 ingredients: a can of soda and a brownie mix.
Mix them up and bake according to the package directions. We used half a can and put ours in a 9x13, so they were a little more dense but still chewy. Some people might not like the texture, but I think it's a good alternative for people that have to avoid egg. If you want it more fluffy, use the entire can.