We use quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter rs=31(1) a.u. and a transition to a ferromagnetic crystal at rs=38(5) a.u. The fully spin-polarized fluid is never stable. We search for, but do not find, the ferromagnetic “hybrid” phase proposed by H. Falakshahi and X. Waintal [ Phys. Rev. Lett. 94 046801 (2005)].