We present a systematic survey of multiple velocity-resolved H2O spectra using Herschel/Heterodyne Instrument for the Far Infrared (HIFI) toward nine nearby actively star-forming galaxies. The ground-state and low-excitation lines (E-up <= 130 K) show profiles with emission and absorption blended together, while absorption-free medium-excitation lines (130 K <= E-up <= 350 K) typically display line shapes similar to CO. We analyze the HIFI observation together with archival SPIRE/PACS H2O data using a state-of-the-art 3D radiative transfer code that includes the interaction between continuum and line emission. The water excitation models are combined with information on the dust and CO spectral line energy distribution to determine the physical structure of the interstellar medium (ISM). We identify two ISM components that are common to all galaxies: a warm (T-dust similar to 40-70 K), dense (n(H) similar to 10(5)-10(6) cm(-3)) phase that dominates the emission of medium-excitation H2O lines. This gas phase also dominates the far-IR emission and the CO intensities for J(up) > 8. In addition, a cold (T-dust similar to 20-30 K), dense (n(H) similar to 10(4)-10(5)cm(-3)), more extended phase is present. It outputs the emission in the low-excitation H2O lines and typically also produces the prominent line absorption features. For the two ULIRGs in our sample (Arp 220 and Mrk 231) an even hotter and more compact (R-s <= 100 pc) region is present, which is possibly linked to AGN activity. We find that collisions dominate the water excitation in the cold gas and for lines with E-up <= 300 K and E-up <= 800 K in the warm and hot component, respectively. Higher-energy levels are mainly excited by IR pumping.