Flax seeds can make awesome binders!
To replace 3 eggs: bring one cup of water and 2 to 3 tablespoons whole flax seeds to a boil. Reduce heat to low and cook for about five minutes, stirring occassionally, until the mixture thickens into goo (similar in texture to egg whites). Strain and cool the goo, and use like eggs.
For cakes, I add the flax goo last, after everything else is mixed togther because it really can firm up a batter. And I usually don't bother to strain the flax seeds out (because it's a pain) unless I'm baking something really fancy.
Ground flax seed recipe (for 1 "egg"): Take 2 tbsp ground flax seed and combine with 3 tbsp water.
You can also use half a banana for 1 "egg".
3 tbsp applesauce = 1 "egg".