Extensive ab initio calculations have been performed using the 6-31G(d,p) and 6-311++G(2d,2p) basis sets for several possible structures of water clusters (H2O)(n), n = 8-20. It is found that the most stable geometries arise from a fusion of tetrameric or pentameric rings. As a result, (H2O)(n), n = 8, 12, 16, and 20, are found to be cuboids, while (H2O)(10) and (H2O)(15) are fused pentameric structures. For the other water clusters (n = 9, 11, 13, 14, and 17-19) under investigation, the most stable geometries can be thought of as arising from either the cuboid or the fused pentamers or a combination thereof. The stability of some of the clusters, namely, n = 8-16, has also been studied using density functional theory. An attempt has been made to estimate the basis set superposition error and zero-point energy correction for such clusters at the Hartree-Fock (HF) level using the 6-311++G(2d,2p) basis set. To ensure that a minimum on the potential-energy surface has been located, frequency calculations have been carried out at the HF level using the 6-31G(d,p) and 6-311++G(2d,2p) basis sets for some of the clusters. Molecular electrostatic potential topography mapping has been employed for understanding the reactivity as well as the binding patterns of some of the structurally interesting clusters.