The horizontal branch (HB) morphology of globular clusters (GCs) is most strongly influenced by metallicity. The second parameter phenomenon, first described in the 1960s, acknowledges that metallicity alone is not enough to describe the HB morphology of all GCs. In particular, astronomers noticed that the outer Galactic halo contains GCs with redder HBs at a given metallicity than are found inside the solar circle. Thus, at least a second parameter was required to characterize HB morphology. While the term "second parameter" has since come to be used in a broader context, its identity with respect to the original problem has not been conclusively determined. Here we analyze the median color difference between the HB and the red giant branch, hereafter denoted as Δ(V - I), measured from Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) photometry of 60 GCs within ~20 kpc of the Galactic center. Analysis of this homogeneous data set reveals that, after the influence of metallicity has been removed from the data, the correlation between Δ(V - I) and age is stronger than that of any other parameter considered. Expanding the sample to include HST ACS and Wide Field Planetary Camera 2 photometry of the six most distant Galactic GCs lends additional support to the correlation between Δ(V - I) and age. This result is robust with respect to the adopted metallicity scale and the method of age determination, but must bear the caveat that high-quality, detailed abundance information is not available for a significant fraction of the sample. Furthermore, when a subset of GCs with similar metallicities and ages is considered, a correlation between Δ(V - I) and central luminosity density is exposed. With respect to the existence of GCs with anomalously red HBs at a given metallicity, we conclude that age is the second parameter and central density is most likely the third. Important problems related to HB morphology in GCs, notably multi-modal distributions and faint blue tails, remain to be explained. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555, under program GO-10775.