We present an analysis of stellar mass estimates for a sample of 25000 galaxies from the COMBO-17 survey over the interval 0.2<z<1.0. We have developed, implemented, and tested a new method of estimating stellar mass-to-light ratios, which relies on redshift and spectral energy distribution (SED) classification from 5 broadband and 12 medium band filters. We find that the majority (>60%) of massive galaxies with M_* > 10^{11} solar masses at all z<1 are non-star-forming; blue star-forming galaxies dominate at lower masses. We have used these mass estimates to explore the evolution of the stellar mass function since z=1. We find that the total stellar mass density of the universe has roughly doubled since z~1. Our measurements are consistent with other measurements of the growth of stellar mass with cosmic time and with estimates of the time evolution of the cosmic star formation rate. Intriguingly, the integrated stellar mass of blue galaxies with young stars has not significantly changed since z~1, even though these galaxies host the majority of the star formation: instead, the growth of the total stellar mass density is dominated by the growth of the total mass in the largely passive galaxies on the red sequence. Comment: Astronomy and Astrophysics in press. 15 pages, 12 figures