A new analysis of the spin rate distribution of asteroids is performed; it attempts to take into account the principal selection effects and studies separately several different sub-samples, chosen according to the asteroid size range and taxonomic classification. The results show strong statistical evidence for a non-Maxwellian character of the overall distribution, mainly due to an excess of slowly rotating objects of small and intermediate size. It is also found that the average spin rate increases with size, while different taxonomic types present distinct features for their distributions. These results can be interpreted in terms of a complex and size-dependent collisional history of asteroids, with widespread fragmentation and the frequent formation of binary or multiple asteroids.