We present measured and calculated differential cross sections, as well as calculated integral cross sections, for elastic electron collisions with CH3F, CHF2F2, CHF3, and CF4. The calculated cross sections were obtained with the Schwinger multichannel method, and a Born-closure procedure was used to improve the differential cross sections for polar systems. Polarization effects were found to be relevant even for systems with moderately large permanent dipole moments, such as CH3F and CHF3. In general, there is good agreement between theory and experiment.652