The data structures and algorithms of a newly developed three-dimensional direct simulation Monte Carlo program are outlined. The code employs an embedded three-level Cartesian mesh accompanied by a cut-cell algorithm to incorporate triangulated surface geometry. A simple and efficient adaptive mesh refinement algorithm that maintains a local cell size and time step consistent with the local mean-free path and local mean-collision time is detailed, along with a cut-cell algorithm that sorts triangulated surface elements into Cartesian cells and uses a Monte Carlo technique to compute the cut volume. Three-dimensional direct simulation Monte Carlo simulations of hypersonic flow over a 70 deg blunted cone geometry at various angles of attack are presented. For a 0 deg angle of attack, direct simulation Monte Carlo solutions are in excellent agreement with other simulations reported in the literature and with experimental results for density field and surface heat flux. New simulation results are presented for three-dimensional flows over the probe geometry at 10 and 30 deg angles of attack where direct simulation Monte Carlo predictions for density field and heat flux are in close agreement with the experiment. The largest discrepancy is found in the heat flux along the windward forebody (for 30 deg angles of attack), where the simulations overpredict the experimental measurements by, at most, 25%.