We discuss the main properties of the Galactic globular cluster (GC) blue straggler stars (BSSs), as inferred from our new catalog containing nearly 3000 BSSs. The catalog has been extracted from the photometrically homogeneous V versus (B-V) color-magnitude diagrams (CMDs) of 56 GCs, based on Wide Field Planetary Camera 2 images of their central cores. In our analysis, we used consistent relative distances based on the same photometry and calibration. The number of BSSs has been normalized to obtain relative frequencies (FBSS) and specific densities (NS) using different stellar populations extracted from the CMD. The cluster FBSS is significantly smaller than the relative frequency of field BSSs. We find a significant anticorrelation between the BSS relative frequency in a cluster and its total absolute luminosity (mass). There is no statistically significant trend between the BSS frequency and the expected collision rate. The value of FBSS does not depend on other cluster parameters, apart from a mild dependence on the central density. Post-core-collapse clusters act like normal clusters as far as the BSS frequency is concerned. We also show that the BSS luminosity function for the most luminous clusters is significantly different, with a brighter peak and extending to brighter luminosities than in the less luminous clusters. These results imply that the efficiency of BSS production mechanisms and their relative importance vary with the cluster mass. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.