We have made precise observations of a thorium-argon hollow cathode lamp emission spectrum in the region between 350nm and 1175nm using a high-resolution Fourier transform spectrometer. Our measurements are combined with results from seven previously published thorium line lists to re-optimize the energy levels of neutral, singly, and doubly ionized thorium (Th I, Th II, and Th III). Using the optimized level values, we calculate accurate Ritz wavelengths for 19874 thorium lines between 250nm and 5500nm (40000/cm to 1800/cm). We have also found 102 new thorium energy levels. A systematic analysis of previous measurements in light of our new results allows us to identify and propose corrections for systematic errors in Palmer & Engleman (1983ats..book.....P) and typographical errors and incorrect classifications in Kerber et al. (2008ApJS..178..374K). We also found a large scatter with respect to the thorium line list of Lovis & Pepe (Cat. J/A+A/468/1115). We anticipate that our Ritz wavelengths will lead to improved measurement accuracy for current and future spectrographs that make use of thorium-argon or thorium-neon lamps as calibration standards.