Five prominent extragalactic water masers have been observed at roughly monthly intervals from 1984 until 1993 to study their temporal characteristics. The observing program at Haystack Observatory comprised five sources: NGC 1068, NGC 3079, NGC 4258, the irregular galaxy IC 10, and IC 133, an H II region complex in M33. The data on two sources, NGC 4258 and IC 10SE, have been presented earlier. All galaxies show strong variability in line strength, line velocity, and line width. The observed variability characteristics support a model with inverted molecular gas located in front of the nuclear source that experiences a variable pump rate and in part amplifies the background continuum. The extragalactic sources have been classified as class I for H II region emission sources in nearby galaxies or class II for mostly powerful emissions from galactic nuclei. In analogy with NGC 4258, the spectral features of class II sources NGC 1068 and NGC 3079 display a drift rate consistent with a compact molecular torus for the emission region.