The roughness of spin-cast polymer films arises from thermally activated capillary waves during preparation and typically amounts to about 0.5 nm(rms) measured on a micrometer-sized surface area. Templating from atomically flat mica substrates allows the creation of polymer films with a surface roughness approaching the molecular scale. Three regimes of spatial frequencies are identified in which the roughness is controlled by different physical mechanisms. We find that frozen-in elastic pressure waves ultimately limit the flatness of polymer films.