What is the best egg-replacer for baking (flaxseed?)?

I highly recommend ener-g egg replacer, but since you say you don't want to go out and buy anything, then I would say go with the flaxseed or the banana. This depends on what you're baking. If you don't mind a little banana flavor in your cooking, then banana makes an awesome alternative. If you're baking something like chocolate-chip cookies, though, and don't want them to taste like bananas, then go with the flaxseed. You have to grind flaxseed up, though, so if you don't have pre-ground seed or if you don't have a grinder, then skip it. you can also use soft tofu very well in some recipes. I've made some amazing brownies using soft tofu instead of eggs.