We present a study of molecular outflows toward a sample of 69 luminous IRAS point sources. The sample is associated with dense molecular gas and has far-infrared luminosities ranging from 10² to 10⁵ L, indicating these objects as regions likely forming high-mass stars. Mapping in the CO J = 2-1 line shows that molecular outflows are ubiquitous in these regions. Most of the outflows have masses of tens of M. The typical dynamical timescale of the flow, without correcting for inclination of the flow axis, is a few times 10⁴ yr. The typical energy in the outflows is 10⁴⁶ ergs, comparable to the turbulent energy in the core. Nearly half of the outflows show spatially resolved bipolar lobes. This indicates that low-mass young stars that coexist in the region are not responsible for the bipolar outflows observed. It is the more massive stars that drive the outflow. The large detection rate of outflows in the region favors an accretion process in the formation of massive stars. The maximum mass-loss rate in the wind is about 10^-4 M yr^-1. If these outflows are driven via accretion, the accretion rate should be as high as a few times 10^-4 M yr^-1. We compare CO outflows with images at near-infrared wavelengths from the Two Micron All Sky Survey (2MASS) archive and find that some outflows are associated with extended emission in the K band, which may be partly due to vibrationally excited H₂ emission at 2.12 μm.