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We have observed 150 regions of massive star formation, selected originally by the presence of a water maser, in the J = 5-4, 3-2, and 2-1 transitions of CS, and 49 regions in the same transitions of C$^{34}$S. Over 90% of the 150 regions were detected in the J = 2-1 and 3-2 transitions of CS and 75% were detected in the J=5-4 transition. We have combined the data with the J = 7-6 data from our original survey (Plume et al. 1992) to determine the density by analyzing the excitation of the rotational levels. Using Large Velocity Gradient (LVG) models, we have determined densities and column densities for 71 of these regions. The gas densities are very high (the mean log of the density is 5.9), but much less than the critical density of the J=7-6 line. Small maps of 25 of the sources in the J = 5-4 line yield a mean diameter of 1.0 pc. The mean virial mass is 3800 solar masses. The mean ratio of bolometric luminosity to virial mass (L/M) is 190, about 50 times higher than estimates using CO emission, suggesting that star formation is much more efficient in the dense gas probed in this study. The gas depletion time for the dense gas is roughly 1.3 x 10^7 yr. We find no statistically significant linewidth--size or density--size relationships in our data. Instead, both linewidth and density are larger for a given size than would be predicted by the usual relationships. We find that the linewidth increases with density, the opposite of what would be predicted by the usual arguments. We estimate that the luminosity of our Galaxy (excluding the inner 400 pc) in the CS J = 5-4 transition is 15 to 23 L_sun, considerably less than the luminosity in this line within the central 100 pc of NGC 253 and M82. In addition, the ratio of far-infrared luminosity to CS luminosity is higher in M82 than in any cloud in our sample.