The Faddeev equations for the three-body bound state are solved directly as three-dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three-body binding energy is calculated for Malfliet-Tjon-type potentials and compared with results obtained from calculations based on partial wave decomposition. The full three-body wave function is calculated as function of the vector Jacobi momenta. It is shown that it satisfies the Schrödinger equation with high accuracy. The properties of the full wave function are displayed and compared to the ones of the corresponding wave functions obtained as finite sum of partial wave components. The agreement between the two approaches is essentially perfect in all respects.