Question

If water were a nonpolar molecule, how would its properties be different?

Answer 1

If water was nonpolar, life as it exists now would be impossible. Water is the means by which ionic substances ( Fe^3+, Na^+, Ca^2+, K^+, etc) and polar molecules are distributed around and in the cells of organisms. 
Water is a major contributor to erosion of mountains because of its polar nature. It is able to dissolve almost all minerals because of its attraction for the positive and negative parts of the minerals that it encounters. 
If it was nonpolar, it would not exist in the solid and liquid state on earth. It is the attraction of the oppositely charged ends of different water molecules that makes it assume the liquid and solid state under the temperature ranges found on earth.