The conjugate base of water, H2O, is the hydroxide ion, OH-. Water only forms a conjugate base in reactions where it acts like an acid, which means it donates a proton. For example, when reacting with ammonia, NH3, the end products are the conjugate base OH- and ammonium, NH4+.
Conjugate bases are the result of an acid donating a proton. Similarly, conjugate acids are the result of a base accepting a proton. Water is unique in that it can act as either a base or acid, depending on the other reactants present. The concept of conjugate acids and bases is rooted in the Bronsted-Lowry theory of acids and bases.