We use nondiffusive, nonrelativistic, test-particle numerical simulations to address the physics of particle acceleration by collisionless shocks. We focus on the importance of the shock normal angle,⟨ θ Bn⟩, in determining the energy spectrum of the accelerated particles. For reasonable parameters, we find that the injection velocity is weakly dependent on the mean shock normal angle and that low-energy particles are readily accelerated to high energies irrespective of⟨ θ Bn⟩. Our results are applicable for shocks that are nearly planar on scales larger than the coherence scale of the upstream magnetic turbulence and for particles whose gyroradii are smaller than this scale. We confirm previous results showing that the acceleration rate is larger for nearly perpendicular shocks compared to parallel shocks. However, we also find that the acceleration rate at parallel shocks moving through large-scale magnetic fluctuations is larger than that predicted by simple first-order Fermi acceleration. Our results can be understood in terms of the nature of the large-scale fluctuations and their effect on particle transport.