We present comprehensive results of large-scale molecular dynamics and Monte Carlo simulations of systems of dense hard spheres at volume fraction phi along the disordered, metastable branch of the phase diagram from the freezing-point phi(f) to random close packing volume phi(c). It is shown that many previous simulations contained deficiencies caused by crystallization and finite-size effects. We quantify the degree of local crystallization through an order parameter and study it as a function of time and initial conditions to determine the necessary conditions to obtain truly random systems. This ordering criterion is used to show that previous methods employed to ascertain the degree of randomness are inadequate. A careful study of the pressure is also carried out along the entire metastable branch. In the vicinity of the random-close packing fraction, we show that the pressure scales as (phi(c)-phi)(-gamma), where gamma = 1 and phi(c) = 0.644 +/- 0.005. Contrary to previous studies, we find no evidence of a thermodynamic glass transition.