The response of forsterite, Mg2SiO4, under dynamic compression is of fundamental importance for understanding its phase transformations and high-pressure behavior. Here, we have carried out an in situ X-ray diffraction study of laser-shocked polycrystalline and single-crystal forsterite (a-, b-, and c-orientations) from 19 to 122 GPa using the Matter in Extreme Conditions end-station of the Linac Coherent Light Source. Under laser-based shock loading, forsterite does not transform to the high-pressure equilibrium assemblage of MgSiO3 bridgmanite and MgO periclase, as has been suggested previously. Instead, we observe forsterite and forsterite III, a metastable polymorph of Mg2SiO4, coexisting in a mixed-phase region from 33 to 75 GPa for both polycrystalline and single-crystal samples. Densities inferred from X-ray diffraction data are consistent with earlier gas-gun shock data. At higher stress, the response is sample-dependent. Polycrystalline samples undergo amorphization above 79 GPa. For - and -oriented crystals, a mixture of crystalline and amorphous material is observed to 108 GPa, whereas the -oriented forsterite adopts an unknown phase at 122 GPa. The first two sharp diffraction peaks of amorphous Mg2SiO4 show a similar trend with compression as those observed for MgSiO3 in both recent static- and laser-driven shock experiments. Upon release to ambient pressure, all samples retain or revert to forsterite with evidence for amorphous material also present in some cases. This study demonstrates the utility of femtosecond free-electron laser X-ray sources for probing the temporal evolution of high-pressure silicate structures through the nanosecond-scale events of shock compression and release.