The Russian-American experiment SAGE began to measure the solar neutrino capture rate with a target of gallium metal in December 1989. Measurements have continued with only a few brief interruptions since that time. In this article we present the experimental improvements in SAGE since its last published data summary in December 2001. Assuming the solar neutrino production rate was constant during the period of data collection, combined analysis of 168 extractions through December 2007 gives a capture rate of solar neutrinos with energy more than 233 keV of $65.{4}_{\ensuremath{-}3.0}^{+3.1}$ (stat) ${}_{\ensuremath{-}2.8}^{+2.6}$ (syst) SNU. The weighted average of the results of all three Ga solar neutrino experiments, SAGE, Gallex, and GNO, is now $66.1\ifmmode\pm\else\textpm\fi{}3.1$ SNU, where statistical and systematic uncertainties have been combined in quadrature. During the recent period of data collection a new test of SAGE was made with a reactor-produced $^{37}\mathrm{Ar}$ neutrino source. The ratio of observed to calculated rates in this experiment, combined with the measured rates in the three prior $^{51}\mathrm{Cr}$ neutrino-source experiments with Ga, is $0.87\ifmmode\pm\else\textpm\fi{}0.05$. A probable explanation for this low result is that the cross section for neutrino capture by the two lowest-lying excited states in $^{71}\mathrm{Ge}$ has been overestimated. If we assume these cross sections are zero, then the standard solar model including neutrino oscillations predicts a total capture rate in Ga in the range of 63 SNU to 66 SNU with an uncertainty of about 4%, in good agreement with experiment. We derive the current value of the neutrino flux produced in the Sun by the proton-proton fusion reaction to be ${\ensuremath{\phi}}_{\mathit{pp}}^{\ensuremath{\bigodot}}=(6.0\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{10}/({\mathrm{cm}}^{2} \mathrm{s})$, which agrees well with the $\mathit{pp}$ flux predicted by the standard solar model. Finally, we make several tests and show that the data are consistent with the assumption that the solar neutrino production rate is constant in time.