The phase transitions exhibited by systems of hard spherocylinders, with a diameter D and cylinder length L, are re-examined with the isothermal-isobaric Monte Carlo (MC-NPT) simulation technique. For sufficiently large aspect ratios (L/D) the system is known to form liquid crystalline phases : isotropic (I), nematic (N), smectic-A (Sm A), and solid (K) phases are observed with increasing density. There has been some debate about the first stable liquid crystalline phase to appear as the aspect ratio is increased from the hard-sphere limit. We show that the smectic-A phase becomes stable before the nematic phase as the anisotropy is increased. There is a transition directly from the isotropic to the smectic-A phase for the system with L/D = 3.2. For larger aspect ratios, e.g., L/D = 4, the smectic-A phase is preceded by a nematic phase. This means that the hard spherocylinder system exhibits I-Sm A-K and I-N-Sm A triple points, the latter occurring at a larger aspect ratio. We also confirm the simulation results of Frenkel [J. Phys. Chem. 92, 3280 (1988)] for the system with L/D = 5, which exhibits isotropic, nematic, smectic-A, and solid phases. All of the phase transitions are accompanied by a discontinuous jump in the density, and are, therefore, first order. In the light of these new simulation results, we re-examine the adequacy of the Parsons [Phys. Rev. A 19, 1225 (1979)] scaling approach to the theory of Onsager for the I-N phase transition. It is gratifying to note that this simple approach gives an excellent representation of both the isotropic and nematic branches, and gives accurate densities and pressures for the I-N phase transition. As expected for such a theory, the corresponding orientational distribution function is not accurately reproduced at the phase transition. The results of the recent Onsager/DFT theory of Esposito and Evans [Mol. Phys. 83, 835 (1994)] for the N-Sm A bifurcation point are also in agreement with the simulation data. It is hoped that our simulation results will be used for comparisons with systems with more complex interactions, e.g., dipolar hard spherocylinders and hard spherocylinders with attractive sites.