Seismic and thermal estimates suggest a highly variable thickness of Precambrian lithosphere (140-350 km), with a bimodal distribution for Archean cratons (~220 km and ~350 km). We discuss the origin of such large variations in lithospheric thickness and examine mechanisms of lithospheric erosion. Our analysis shows that the horizontal and vertical dimensions of Archean cratons are strongly correlated: larger cratons have thicker lithosphere. We investigate the hypothesis that plate motions influence the structure of deep lithospheric keels (or vice versa). The analysis shows that plates having deeper Archean keels move slower. The basal drag model of lithosphere erosion (Sleep, 2001) is tested as a means of explaining the present-day bimodal distribution of lithospheric thicknesses of the Archean cratons. In agreement with theoretical predictions, we find that lithospheric thickness in Archean keels is proportional to the square root of the ratio of the craton length (along the direction of plate motion) to the plate velocity. These results show that the basal drag model provides a viable explanation for the variation in thickness of Archean cratonic roots. Large cratons are more stable with respect to basal erosion caused by a horizontal movement of lithospheric plates over the underlying mantle. Large cratons with thick keels and low plate velocities are less eroded by the basal drag than small fast-moving cratons. Basal drag may have varied in magnitude over the past 4 Ga. Higher mantle temperatures in the Archean would have resulted in lower mantle viscosity. This in turn would have reduced basal drag and basal erosion, and promoted the preservation of thick (>300 km) Archean keels, even if plate velocities were high during the Archean.