Images of films (500-1100 angstrom thick) of several nonconducting polymers, spin cast on Au-coated silicon wafers, have been obtained with a scanning tunneling microscope (STM). Imaging was not possible if films were cast on SiO2 and depends on scan rate : when a critical value was exceeded, the image became grossly degraded and a damaged spot under the tip was optically visible. The damage threshold was generally higher for Pt/Ir tips than for ion-implanted diamond. Damage was not observed when stable, repeatable images were obtained; these showed mean roughness of approximately 5 angstrom, and 10-50-angstrom undulations 100-300 angstrom wide. Atomic force microscopy (AFM) images were also obtained and confirm the STM data. Grooves several nanometers deep were formed and imaged with the same tip (ion-implanted diamond), without tip degradation. The mechanism of imaging is postulated to involve a combination of field-assisted electron transfer and pressure-induced effects.