We report homogeneous spectroscopic determinations of the effective temperature, metallicity, and projected rotational velocity for the host stars of 56 transiting planets. Our analysis is based primarily on the Stellar Parameter Classification (SPC) technique. We investigate systematic errors by examining subsets of the data with two other methods that have often been used in previous studies (SME and MOOG). The SPC and SME results, both based on comparisons between synthetic spectra and actual spectra, show strong correlations between temperature, [Fe/H], and log g when solving for all three quantities simultaneously. In contrast the MOOG results, based on a more traditional curve-of-growth approach, show no such correlations. To combat the correlations and improve the accuracy of the temperatures and metallicities, we repeat the SPC analysis with a constraint on log g based on the mean stellar density that can be derived from the analysis of the transit light curves. Previous studies that have not taken advantage of this constraint have been subject to systematic errors in the stellar masses and radii of up to 20% and 10%, respectively, which can be larger than other observational uncertainties, and which also cause systematic errors in the planetary mass and radius. ; Comment: 13 pages in emulateapj format, including figures and tables. Accepted for publication in The Astrophysical Journal. The complete tables 5 and 7 will appear in the electronic edition of the Journal. Comment added in Sect. 4.2 about the dependence of the correlations on temperature