The IRAS data base on asteroid albedos and diameters has been used to derive size distributions for a set of about 4000 numbered main-belt asteroids and for various subsets defined according to the semimajor axis range and family membership. Different procedures have been used to obtain albedo estimates for the (mostly small) members of the sample not observed by IRAS, allowing us to assess the sensitivity of the derived size distributions to the assumptions used for this purpose. The results show that, apart from the Flora zone in the inner belt, non-family asteroids always have size distributions characterized by a strong change in slope at diameters almost-equal-to 150 km, with the differential power-law distribution exponent passing from values around 3 or more at large sizes, to almost-equal-to 1 at smaller ones. In the Flora region, where the sample is complete down to about 18 km (contrasting with 44 km for the whole asteroid population), a steep slope is also observed at small sizes. A similar feature is typical of the most populous families. While the size distribution of large bodies has probably been little affected by collisional evolution, it seems likely that most family members and Flora asteroids are fragments from catastrophic impacts, with a size distribution close to that found after laboratory impact experiments. For the other main-belt asteroids, the flatter slope in the intermediate diameter range between almost-equal-to 30 and 150 km is either due to the influence of self-gravity on the collisional outcomes, or is a remnant of the 'primordial' distribution. Collisional evolution models, however, can approximately reproduce the observed overall distribution starting from very different initial populations. Thus, the size distribution data alone do not effectively constrain the initial distribution and the intensity of the collisional process.
