In plasmas including fusion plasmas, various molecules exist in neutral and ionized forms and interact with each other as well as with electrons and photons. To properly understand and control the plasma, cross sections of these interactions are needed. Many of these interaction processes are initiated by electron scattering, and therefore an understanding of the electron scattering with atoms and molecules in plasma and their associated cross sections are very important to understanding of plasma. In this paper we evaluate the total electron scattering cross sections (TCSs) for eight plasma-relevant molecules - C2F6, CF3Cl, CF3I, C3F8, c-C4F8, CH4, C2H4, and C2H6 - both to present recommended TCSs and to demonstrate evaluation methods. We have reviewed data from the literature up to mid-2012 and the energy range of interest is up to and including 100 eV. TCSs for these common molecules, which are supposed to be in the best situation among the scattering cross sections, are far from satisfactory. More activities in measurements of cross sections are required.