We report the results of a spectropolarimetric survey of the CfA and 12 μm samples of Seyfert 2 (S2) galaxies. Polarized (hidden) broad-line regions (HBLRs) are confirmed in a number of galaxies, and several new cases (F02581-1136, MCG -3-58-7, NGC 5995, NGC 6552, NGC 7682) are reported. The 12 μm S2 galaxy sample shows a significantly higher incidence of HBLRs (50%) than its CfA counterpart (30%), suggesting that the latter may be incomplete in hidden active galactic nuclei. Compared to the non-HBLR S2 galaxies, the HBLR S2 galaxies display distinctly higher radio power relative to their far-infrared output and hotter dust temperature as indicated by the f25/f60 color. However, the level of obscuration is indistinguishable between the two types of S2 galaxies. These results strongly support the existence of two intrinsically different populations of S2 galaxies: one harboring an energetic, hidden S1 nucleus with a broad-line region and the other a ``pure'' S2 galaxy, with a weak or absent S1 nucleus and a strong, perhaps dominating starburst component. Thus, the simple purely orientation-based unification model is not applicable to all Seyfert galaxies.