A theoretical model for electron-impact ionization cross sections, which has been developed primarily for atoms and atomic ions, is applied to neutral molecules. The new model combines the binary-encounter theory and the Bethe theory for electron-impact ionization, and uses minimal theoretical data for the ground state of the target molecule, which are readily available from public-domain molecular structure codes such as GAMESS. The theory is called the binary-encounter Bethe (BEB) model, and does not, in principle, involve any adjustable parameters. Applications to 19 molecules, including H-2, NO, CH2, C6H6, and SF6, are presented, demonstrating that the BEB model provides total ionization cross sections by electron impact from threshold to several keV with an average accuracy of 15% or better at the cross section peak, except for SiF3. The BEB model can be applied to stable molecules as well as to transient radicals.