It is has been established that the excess electrons in small (i.e., n <= 7) (H2O)(n)(-) clusters are bound in the dipole field of the neutral cluster and, thus, exist as surface states. However, the motifs for the binding of an excess electron to larger water clusters remain the subject of considerable debate. The prevailing view is that electrostatic interactions with the "free" OH bonds of the cluster dominate the binding of the excess electron in both small and large clusters. In the present study, a quantum Drude model is used to study selected (H2O)(n)(-) clusters in the n = 12-24 size range with the goal of elucidating different possible binding motifs. In addition to the known surface and cavity states, we identify a new binding motif, where the excess electron permeates the hydrogen-bonding network. It is found that electrostatic interactions dominate the binding of the excess electron only for isomers with large dipole moments, whereas in isomers without large dipole moments polarization and correlation effects dominate. Remarkably, for the network-permeating states, the excess electron binds even in the absence of electrostatic interactions.