Wolf-Rayet (WR) stars are evolved massive stars, and the relative number of WC-type and WN-type WRs should vary with metallicity, providing a sensitive test of stellar evolutionary theory. The observed WC/WN ratio is much higher than that predicted by theory in some galaxies but this could be due to observational incompleteness for WN types, which have weaker lines. Previous studies of M33's WR content show a galactocentric gradient in the relative numbers of WCs and WNs, but only small regions have been surveyed with sufficient sensitivity to detect all of the WNs. Here, we present a sensitive survey for WRs covering all of M33, finding 55 new WRs, mostly of WN type. Our spectroscopy also improves the spectral types of many previously known WRs, establishing in one case that the star is actually a background quasar. The total number of spectroscopically confirmed WRs in M33 is 206, a number we argue is complete to ~5%, with most WRs residing in OB associations, although ~2% are truly isolated.