What you need to substitute is the binding ability of the eggs. There are a few ways to do this...
There are a variety of seeds that produce mucilage when soaked in water. This sticky substance can work very well to bind baked goods together. To use, you soak the seeds or seed meal in water until the water becomes thick. If whole seeds are used, the water may be heated to speed up the process. Some of the most common seeds that have this characteristic are flax, chia, and buckwheat.
An alternate method that will change the characteristic of your pancakes a bit is to incorporate something that contains pectin. This includes many fruits: canned pumpkin, mashed banana, apple sauce, many jams and preserves, etc. The pectin will serve as your binder.
Some eggless pancake recipes also call for small amounts of corn starch (which has some mild binding abilities) or cider vinegar (which aids leavening and helps to tighten dough, but doesn't really bind on it's own).