A detailed study of interstellar polarization efficiency toward molecular clouds is used to attempt discrimination between grain alignment mechanisms in dense regions of the ISM. Background field stars are used to probe polarization efficiency in quiescent regions of dark clouds, yielding a dependence on visual extinction well-represented by a power law. No significant change in this behavior is observed in the transition region between the diffuse outer layers and dense inner regions of clouds, where icy mantles are formed, and we conclude that mantle formation has little or no effect on the efficiency of grain alignment. Young stellar objects generally exhibit greater polarization efficiency compared with field stars at comparable extinctions, displaying enhancements by factors of up to 6. Of the proposed alignment mechanisms, that based on radiative torques appears best able to explain the data. The attenuated external radiation field accounts for the observed polarization in quiescent regions, and radiation from the embedded stars themselves may enhance alignment in the lines of sight to YSOs. Enhancements in polarization efficiency observed in the ice features toward several YSOs are of greatest significance, as they demonstrate efficient alignment in cold molecular clouds associated with star formation.