We have conducted spectropolarimetry of 12 type II (obscured) quasar candidates selected from the spectroscopic database of the Sloan Digital Sky Survey based on their emission line properties. Polarization was detected in all objects, with nine being highly polarized (> 3%) and with polarization reaching as high as 17% in two objects. Broad lines were detected in the polarized spectra of five objects. These observations prove beyond a reasonable doubt that the objects in our sample are indeed type II quasars, in that they harbor luminous UV-excess AGNs in their centers and that the direct view to the AGN is highly obscured. For three of the objects in this paper, we have obtained HST images in three bands. The HST observations, combined with the spectropolarimetry data, imply that scattering off material outside the obscuration plane is the dominant polarization mechanism. In all three objects the sizes of scattering regions are a few kpc. For one object, the extent of the scattering region, coupled with the characteristics of the polarized spectrum, argue strongly that dust scattering rather than electron scattering dominates the polarized light. Our observations are well-described by the basic orientation-based unification model of toroidal obscuration and off-plane scattering, implying that the model can be extended to include at least some high-luminosity AGNs.