We present ab initio molecular dynamics simulations for high-density hydrogen (rs=1.78-1.31, P≊35–150 GPa). Protons are treated as classical point charges and electrons in local density functional theory. The basic structural entity in this density range is still the hydrogen molecule but applying pressure changes the molecular ordering drastically. Molecules line up to form filaments and eventually planes, where intermolecular distances become comparable to the H2 bond length. The phase diagram is strongly temperature dependent, and many different structures with very similar stability exist.