Previous work (Rutledge et al., 2000ApJS..131..335R) statistically identified 5492 optical counterparts, with >~90% confidence, from among the ~18000 X-ray sources appearing in the ROSAT All-Sky Survey Bright Source Catalog (RASS BSC; Voges et al. 1999, Cat. <IX/10>). Using low-resolution spectra in the wavelength range 3700-7900{AA}, we present spectroscopic classifications for 195 of these counterparts which have not previously been classified. Of these 195, we find 168 individual stars of F, G, K, or M type, 6 individual stars of unknown type, 6 double stars, 6 AGNs or galaxies, and 7 unclassifiable objects; the spectra of the 2 remaining objects were saturated.