In this work we present a theoretical study on electron scattering by both polar and nonpolar polyatomic molecules in the low-energy range. More specifically, we report calculated elastic and rotationally inelastic differential cross sections for electron scattering by CH4, H2O, and H2S in the (2.14-30)-eV range. Exact static-exchange plus model correlation-polarization potentials are used to represent the electron-molecule interaction. The Schwinger variational iterative method is used to solve the scattering equations. In addition, the adiabatic-nuclei-rotation approximation is applied to calculate rotational cross sections. The comparison of our calculated results with experimental and other theoretical data available in the literature is encouraging.