The Stranski-Krastanov growth mode of Ge thin films on Si and the clustering behavior of Ge on calcium fluoride have been exploited to grow self-assembled nanocrystals by molecular beam epitaxy. The growth of the samples was monitored in situ with RHEED, and they were analyzed ex situ with AFM and RBS. For each system (Ge/Si and Ge/CaF2/Si), the dependence of Ge islanding on substrate temperature and on substrate misorientation was studied. When grown on Si(111) at temperatures between 500°C and 700°C, Ge clusters nucleated at step edges on vicinal wafers and nucleated homogeneously on on-axis wafers. Above 600°C, no transition to a spotty RHEED pattern, which would be expected for island growth, was observed for the vicinal samples. Ge grown at 500°C on on-axis Si(111) formed islands with a relatively narrow size distribution, typically 160nm in diameter and 10nm to 20nm in height. When grown on a CaF2 buffer layer, Ge islands nucleated homogeneously at a substrate temperature of 750°C, resulting in randomly distributed, oblate crystallites approximately 100nm to 200nm in diameter. At 650°C and 700°C, although we still observed many randomly distributed, small crystallites, most islands nucleated at step bunches and had a length scale of over 500nm.