We examine height distribution functions (height histograms) of kinetically roughened metal films, making use of STM data for vapor-deposited Ag on quartz. The height distribution of the raw data is Gaussian to quite high accuracy. However, if one averages each height over a region of length scale L, the resulting distributions deviate increasingly from Gaussian behavior, becoming skewed as L increases. We quantified this behavior by means of moments of the distribution; with increasing L a non-negligible third moment appears. The responsible morphology is minima that tend to form steep valleys or deep pits while the corresponding (at the same height above the average) maxima tend to form rounded hilltops. Skewed height distributions have been predicted on the basis of model calculations, but not previously observed to our knowledge.