We present results of a search for (CO)-C-12 (J = 1-0) high-velocity line wings toward 122 high-mass star formation regions with the NRAO 12 m telescope. Of the 94 sources for which we obtained data suitable for interpretation of low-intensity line wings, fully 90% are associated with high-velocity (HV) gas in the beam. Ten percent have little or no HV gas (full width [FW] less than 15 km s(-1) at the 1 sigma T-A* level), 49% have FWs between 15 and 30 km s(-1) 30% have FWs between 30 and 45 km s(-1), and 11% have FWs greater than (CO)-C-12 (J = 1-0) full widths are generally substantially larger than those seen 45 km s(-1). We find that the toward low-mass stars. If the HV gas is due to bipolar outflows, then these results indicate that molecular outflows are a common property of newly formed massive stars, similar to the findings for low-mass stars. Two high-mass star formation regions with strong (CO)-C-12 (J = 1-0) line wings, G25.65+1.05 and G240.31+0.07, were identified during the survey and mapped with the NRAO 12 m telescope. Each field of view contains an ultracompact H II region located on or near the flow axis of a massive and energetic bipolar outflow. The molecular outflows associated with these sources, like those associated with other massive-star formation regions, have several times more mass and momentum in their flows and similar to 1 order of magnitude greater energies and luminosities than those associated with low-mass stars.