We measure the frequency of bulk gas-stellar counterrotation in a sample of 67 galaxies drawn from the Nearby Field Galaxy Survey, a broadly representative survey of the local galaxy population down to M-B similar to -15. We detect four counterrotators among 17 E/S0's with extended gas emission In (24(-6)(+8)%). contrast, we find no clear examples of bulk counterrotation among 38 Sa-Sbc spirals, although one Sa does show peculiar gas kinematics. This result implies that, at 95% confidence, no more than 8% of Sa-Sbc spirals are bulk counterrotators. Among types Sc and later, we identify only one possible counterrotator, a Magellanic irregular. We use these results together with the physical properties of the counterrotators to constrain possible origins for this phenomenon.