Electrons and positrons in storage rings have natural polarization which is perpendicular to the beam direction. Effects of the transverse polarization to azimuthally integrated cross sections are studied. In the standard model, the polarization does not affect the cross section up to a correction proportional to the electron mass, which is negligible at high energies. This fact is closely related to the chiral symmetry of the standard model. It is not necessarily true if there are new interactions beyond the standard model. Polarization effects in composite and supersymmetric models are studied in detail. New particles such as scalar bosons and excited electrons in composite models can give nonzero polarization effects. In supersymmetric theories, the transverse polarization is useful to probe the mixing of the scalar-electron states. The nonvanishing effects are connected to the breaking of the chiral symmetry by the new interactions.