I was highly allergic to dairy as a child and my mom always gave me soy milk until I developed an allergy to that as well. I can recommend rice milk. It doesn't have too strong a flavor (unless you get a flavored variety, I think they make vanillas and chocolates and things now) although it's a bit on the watery side. Also, in some cases, like in making a cake or something, you can use an applesauce/water/oil combination to compensate for the milk and eggs. The resulting product will be denser but I've always thought it's better than going without.
