The spin asymmetry and integrated spin-unresolved cross sections for the electron-impact ionization of atomic hydrogen are studied. The influence of individual final-state interactions on these quantities is elucidated by investigating the collision process within the plane-wave impulse approximation, the first Born approximation and within an independent Coulomb particle model. The predictions of the latter approximation for the shape and magnitude of the spin asymmetry are in good agreement with experimental data over the entire measured energy range. The effects of final-state electronic correlations are investigated by the inclusion of the electronic Coulomb density-of-states factor as well as by employing a three-body Coulomb wave-function for the description of the final state. For ionization of hydrogen-like ions the calculated asymmetry parameter has a positive slope near threshold indicating that such an energy dependence is due to the electron-nucleus interactions. At threshold the results are analyzed in light of the Wannier theory of threshold ionization.