A stochastic simulation method employing suitable experimentally based cross sections has been developed for probing the spatial distribution of energy loss and the trajectory of 100 eV to 1 MeV electrons in gaseous and liquid water. Elastic collisions and large-energy-loss inelastic collisions strongly influence the passage of electrons such that the separation between the initial and final (E = 25 eV) position is considerably smaller than the path length. At all energies, the mean axial and the mean radial penetrations are somewhat similar, however, the former is strongly influenced by inelastic collisions and the latter by elastic collisions. The effect of phase on the density-normalized range is small for energetic electrons, but differences are apparant at the lowest energies, <2 keV. The spatial distribution of energy deposition shows a marked dependence on electron energy. The spatial dependence of radial energy deposition and dose distributions in the axial and radial directions have been calculated.