Self-assembled GaAs nanowires have been grown on Si by molecular beam epitaxy without the use of any outside metal catalyst. The growth occurs on Si facets obtained by the cleavage of Si(100) substrates. The growth has been obtained with or without Ga pre-deposition. In both cases two kinds of nanowires have been obtained. The wires of the first type clearly present a Ga droplet at their free end and have a lattice structure that is wurtzite for wide regions beneath the Ga droplet. The second type, in contrast, ends with pyramidally shaped GaAs and has a crystal lattice that is mainly zincblende with only a few and small wurtzite regions, if any. The Ga-ended nanowires are longer than the others and thinner on average. The experimental findings suggest that the two types of nanowires grow after different growth processes.