We have studied the ground-state properties of the half-filled Hubbard model on the triangular lattice by means of the slave-boson technique. The combined effects of high correlation and frustration in this non-bipartite lattice produce a rich phase diagram, including paramagnetic, commensurate spiral, and linear spin-density-wave phases, as well as a metal-insulator transition. Unlike previous Hartree-Fock studies of this model, the slave-boson technique predicts no metallic incommensurate spiral state to be the stable ground state in any region of parameter space.