We have studied the formation mechanisms and morphological features of Ge islands grown on Si(001) substrates using gas source molecular beam epitaxy (GSMBE). The size, the shape and the number density of Ge islands show drastic changes when altering parameters such as growth temperature, Ge coverage and Si spacer layer thickness within Ge/Si multilayers. The results also show that certain conditions exist which can produce a large number of relatively small pyramidal islands which are thought to be energetically unstable. Moreover, only the hut-clusters, which are characteristic of low temperature growth, show ordering in vertically stacked Ge layers, with a concomitant shape change to well-organized very small pyramids.