We test the hypothesis that peak ground velocity (PGV) has an upper bound independent of earthquake magnitude and that this bound is controlled primarily by the strength of the seismogenic crust. The highest PGVs, ranging up to several meters per second, have been measured at sites within a few kilometers of the causative faults. Because the database for near-fault PGV is small, we use earthquake slip models, laboratory experiments, and evidence from a mining-induced earthquake to investigate the factors influencing near-fault PGV and the nature of its scaling. For each earthquake slip model we have calculated the peak slip rates for all subfaults and then chosen the maximum of these rates as an estimate of twice the largest near-fault PGV. Nine slip models for eight earthquakes, with magnitudes ranging from 6.5 to 7.6, yielded maximum peak slip rates ranging from 2.3 to 12 m/sec with a median of 5.9 m/sec. By making several adjustments, PGVs for small earthquakes can be simulated from peak slip rates measured during laboratory stick-slip experiments. First, we adjust the PGV for differences in the state of stress (i.e., the difference between the laboratory loading stresses and those appropriate for faults at seismogenic depths). To do this, we multiply both the slip and the peak slip rate by the ratio of the effective normal stresses acting on fault planes measured at 6.8 km depth at the KTB site, Germany (deepest available in situ stress measurements), to those acting on the laboratory faults. We also adjust the seismic moment by replacing the laboratory fault with a buried circular shear crack whose radius is chosen to match the experimental unloading stiffness. An additional, less important adjustment is needed for experiments run in triaxial loading conditions. With these adjustments, peak slip rates for 10 stick-slip events, with scaled moment magnitudes from -2.9 to 1.0, range from 3.3 to 10.3 m/sec, with a median of 5.4 m/sec. Both the earthquake and laboratory results are consistent with typical maximum peak slip rates averaging between 5 and 6 m/sec or corresponding maximum near-fault PGVs between 2.5 and 3 m/sec at seismogenic depths, independent of magnitude. Our ability to replicate maximum slip rates in the fault zones of earthquakes by adjusting the corresponding laboratory rates using the ratio of effective normal stresses acting on the fault planes suggests that the strength of the seismogenic crust is the important factor limiting the near-fault PGV.