Identified charged-particle spectra of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}^{\ifmmode\pm\else\textpm\fi{}}$, $p$, and $\overline{p}$ at midrapidity ($|y|<0.1$) measured by the $\mathit{dE}/\mathit{dx}$ method in the STAR (solenoidal tracker at the BNL Relativistic Heavy Ion Collider) time projection chamber are reported for $\mathit{pp}$ and $d+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV and for $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4, 130, and 200 GeV. Average transverse momenta, total particle production, particle yield ratios, strangeness, and baryon production rates are investigated as a function of the collision system and centrality. The transverse momentum spectra are found to be flatter for heavy particles than for light particles in all collision systems; the effect is more prominent for more central collisions. The extracted average transverse momentum of each particle species follows a trend determined by the total charged-particle multiplicity density. The Bjorken energy density estimate is at least several GeV/${\mathrm{fm}}^{3}$ for a formation time less than 1 fm/$c$. A significantly larger net-baryon density and a stronger increase of the net-baryon density with centrality are found in $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 GeV than at the two higher energies. Antibaryon production relative to total particle multiplicity is found to be constant over centrality, but increases with the collision energy. Strangeness production relative to total particle multiplicity is similar at the three measured RHIC energies. Relative strangeness production increases quickly with centrality in peripheral $\mathrm{Au}+\mathrm{Au}$ collisions, to a value about 50% above the $\mathit{pp}$ value, and remains rather constant in more central collisions. Bulk freeze-out properties are extracted from thermal equilibrium model and hydrodynamics-motivated blast-wave model fits to the data. Resonance decays are found to have little effect on the extracted kinetic freeze-out parameters because of the transverse momentum range of our measurements. The extracted chemical freeze-out temperature is constant, independent of collision system or centrality; its value is close to the predicted phase-transition temperature, suggesting that chemical freeze-out happens in the vicinity of hadronization and the chemical freeze-out temperature is universal despite the vastly different initial conditions in the collision systems. The extracted kinetic freeze-out temperature, while similar to the chemical freeze-out temperature in $\mathit{pp}$, $d+\mathrm{Au}$, and peripheral $\mathrm{Au}+\mathrm{Au}$ collisions, drops significantly with centrality in $\mathrm{Au}+\mathrm{Au}$ collisions, whereas the extracted transverse radial flow velocity increases rapidly with centrality. There appears to be a prolonged period of particle elastic scatterings from chemical to kinetic freeze-out in central $\mathrm{Au}+\mathrm{Au}$ collisions. The bulk properties extracted at chemical and kinetic freeze-out are observed to evolve smoothly over the measured energy range, collision systems, and collision centralities.
