We expect the evolution of massive stars to be strongly influenced by mass loss and hence to be sensitive to metallicity. It should be possible to test this "Conti scenario" be comparing the populations of evolved massive stars among the Local Group galaxies, but such investigations have been hampered by incompleteness. In a previous paper, we presented results of a new survey for red supergiants (RSGs) in selected regions of the Local Group galaxies M33, M31, and NGC 6822. In the present paper, we survey eight fields in M33 for Wolf-Rayet stars (WRs), using interference-filter imaging with a CCD to select candidates. Follow-up spectroscopy is used to confirm 22 newly found WR stars, 21 of WN type. We establish that our survey would readily detect WRs as weak-lined as any known, and we conclude that our survey is essentially complete. This survey confirms suspicions that the previous photographic surveys were only 50% complete for WN-type WRs and allows us to combine the data with equally complete samples on other Local Group galaxies. We find that the relative number of WC- and WN-type WRs correlates extremely well with metallicity, varying by a factor of 3 with galactocentric distance within the plane of M33, and continuing the trend to lower and higher metallicity galaxies. The WC/WN ratio within 3 kpc of the sun is slightly above this trend, and we argue that WN stars are underrepresented in this sample. The WC/WN ratio is anomalously high in IC 10, given its low metallicity, and we demonstrate that this is not because of selection effects but is likely caused by IC 10's current status as a starburst system. We examine the spectral properties of WC stars within these galaxies, confirming the previously reported trends that the spectral lines are stronger and broader in regions of lower metallicity. We suggest that the different WC spectral subclasses do not primarily indicate different physical properties for these stars but rather are simply a reflection of the effect that the initial metal abundances has had on the stellar wind structure. Finally, we compare the luminous RSGs with WRs in these galaxies. We find that there is a very strong correlation of the relative numbers of RSGs and WRs with metallicity, in the sense predicted by Maeder, Lequeux, & Azzopardi: at lower metallicities the fraction of luminous (Mbol < -7) RSGs is higher, with a factor of 6 change within the disk of M33 [Δ log (O/H) = 0.35 dex], and a factor of ~10 change from M31 (or the inner portions of M33) to NGC 6822 [Δ log (O/H) = 0.5 dex]. This is easily explained by the Conti scenario in terms of massive stars spending proportionately less of their He-burning lifetimes as RSGs rather than WRs at higher metallicities and hence higher mass-loss rates. Finally, we note that the presence of luminous RSGs and WRs stars is extremely well correlated for the OB associations in M31 and M33: where one finds one, one finds the other. To the extent that an association is strictly coeval, this argues that some stars of 15 M☉ and above indeed do go through both RSG and WR stages. The presence of WR stars of both WN and WC types in the same associations as luminous RSGs further suggests that some WCs, at least, have gone through the RSG phase. We include an Appendix providing a complete catalog of confirmed WR stars in Local Group galaxies beyond the Magellanic Clouds.
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