We have conducted a spectroscopic survey of a magnitude-limited sample of O stars to search for intrinsic absorption line profile variations, particularly those attributable to nonradial pulsations. Our final sample consists of 30 stars that cover the full range of luminosity classes for spectral types between O4 and O9.7. For these objects, we obtained high-resolution, high signal-to-noise ratio spectroscopic time series of the C IV λλ580l, 5812 doublet, and the He λ5876 triplet. These time series typically consist of 20 spectra per object, and sample timescales ranging from a few hours to ∼1 week. We developed a new technique, temporal variance spectrum analysis, to detect line-profile variations in these data in an objective, statistically rigorous manner.As the primary result of this survey, we report the detection of statistically significant line profile-variations in at least one of the absorption lines for 77% (23130) of our sample. The incidence and amplitude of variability increase with increasing stellar radius and luminosity, so that all the supergiants in our sample exhibit line-profile variations and, conversely, the nonvariable stars are mostly dwarfs. We found no statistically significant line profile variability for dwarfs earlier than O7. The observed distribution of line-profile variables in the H-R diagram agrees approximately with the predicted domain of strange-mode oscillations, even though many of the variations in the spectra of supergiants must, in the first instance, arise in the stellar wind. We discuss ways of reconciling these two, apparently contradictory, aspects of the observed activity in terms of mechanisms that causally link variations in the stellar photosphere to the formation of structure in the stellar wind, especially the strong line-driven instability. Although the true nature of the widespread line-profile variability remains an open issue, it seems likely that pulsation is responsible for much of the observed activity.