The spin rate distribution of main belt/Mars crossing (MB/MC) asteroids with diameters 3-15 km is uniform in the range from f = 1 to 9.5 d-1, and there is an excess of slow rotators with f < 1 d-1. The observed distribution appears to be controlled by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The magnitude of the excess of slow rotators is related to the residence time of slowed down asteroids in the excess and the rate of spin rate change outside the excess. We estimated a median YORP spin rate change of ≈ 0.022   d-1 / Myr for asteroids in our sample (i.e., a median time in which the spin rate changes by 1 d-1 is ≈ 45   Myr), thus the residence time of slowed down asteroids in the excess is ≈ 110   Myr. The spin rate distribution of near-Earth asteroids (NEAs) with sizes in the range 0.2-3 km (∼5 times smaller in median diameter than the MB/MC asteroids sample) shows a similar excess of slow rotators, but there is also a concentration of NEAs at fast spin rates with f = 9 - 10   d-1. The concentration at fast spin rates is correlated with a narrower distribution of spin rates of primaries of binary systems among NEAs; the difference may be due to the apparently more evolved population of binaries among MB/MC asteroids. © 2008 Elsevier Inc. All rights reserved.