We derive secular trends in upper thermospheric density from the historical orbital elements of 27 long-lived, near-Earth space objects. The results cover all levels of solar activity during the period 1996--2001, and each object indicates a long-term decrease of total mass density. The observed trends increase with increasing height from 200--700 km and are largest for solar minimum conditions; average values range from -2% to -5% per decade. The trends are largely independent of geomagnetic activity, local time, latitude, and season. We examine several possible sources of error in our results and conclude that none of them can individually account for the observed trends. The trends that we obtain are qualitatively, and in some cases quantitatively, consistent with available theoretical predictions of density decreases associated with the cooling effect of increased greenhouse gas concentrations.