Context. Rotation is of key importance for the evolution of massive star, including their fate as supernovae or gamma-ray bursts. However, the rotational velocities of OB stars are difficult to determine. Aims: Based on our own data for 31 Galactic O stars and incorporating similar data for 86 OB supergiants from the literature, we aim at investigating the properties of rotational and extra line-broadening as a function of stellar parameters and at testing model predictions about the evolution of stellar rotation. Methods: Fundamental stellar parameters were determined by means of the code FASTWIND. Projected rotational and extra broadening velocities, vsini and ΘRT, originate from a combined Fourier transform and the goodness-of-fit method. Model calculations published previously were used to estimate the initial evolutionary masses, Mevolinit. Results: The sample O stars with Mevolinit ≳ 50 M⊙ rotate with less that 26% of their break-up velocity, and they also lack slow rotators (vsini ≲ 50 km s-1). For the more massive stars (Mevolinit ≥ 35 M⊙) on the hotter side of the bi-stability jump, the observed and predicted rotational rates agree quite well; for those on the cooler side of the jump, the measured velocties are systematically higher than the predicted ones. In general, the derived ΘRT values decrease toward cooler Teff, whilst for later evolutionary phases they appear, at the same vsini, higher for high-mass stars than for low-mass ones. None of the sample stars shows ΘRT ≥ 110 km s-1. For the majority of the more massive stars, extra broadening either dominates or is in strong competition with rotation. Conclusions: For OB stars of solar metallicity, extra broadening is important and has to be accounted for in the analysis. When appearing at or close to the zero-age main sequence, most of the single and more massive stars rotate slower than previously thought. Model predictions for the evolution of rotation in hot massive stars may need to be updated. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, under programme ID 072.D-0196.