Simulated annealing methods have been used with the effective fragment potential to locate the lowest energy structures for the water clusters (H2O)(n) with n=6, 8, 10, 12, 14, 16, 18, and 20. The most successful method uses a local minimization on each Monte Carlo step. The effective fragment potential method yielded interaction energies in excellent agreement with those calculated at the ab initio Hartree-Fock level and was quite successful at predicting the same energy ordering as the higher-level perturbation theory and coupled cluster methods. Analysis of the molecular interaction energies in terms of its electrostatic, polarization, and exchange-repulsion/charge-transfer components reveals that the electrostatic contribution is the dominant term in determining the energy ordering of the minima on the (H2O)(n) potential energy surfaces, but that differences in the polarization and repulsion components can be important in some cases.