This paper discusses the growth of silicon nanostructures on silicon (100), (110) and (111) substrates by electron beam annealing. The nanofabrication procedure involves annealing of the untreated Si substrates in the temperature range 750°C - 1200°C using a raster scanned 20 keV electron beam. Nanostructuring occurs as a result of kinetic amplification of the surface disorder induced by thermal decomposition of the native oxide. Pyramidal and truncated pyramidal nanocrystals were observed on Si(100) surfaces. The nanostructures are randomly distributed over the entire surface and square-based, reflecting the two-fold symmetry of the substrate surface. Similar square-based pyramidal structures with four equivalent facets are observed following nanostructuring of Si(110). With Si(111), nanostructure growth occurs preferentially along step-edges formed on the vicinal surfaces. Significant differences in nanostructure shapes formed on step-edges and terraces are related to the different growth mechanisms on the unreconstructed and 7x7 reconstructed domains respectively.