Various different physical processes contribute to the star formation and stellar mass assembly histories of galaxies. One important approach to understanding the significance of these different processes on galaxy evolution is the study of the stellar population content of today's galaxies in a spatially resolved manner. The aim of this paper is to characterize in detail the radial structure of stellar population properties of galaxies in the nearby universe, based on a uniquely large galaxy sample, considering the quality and coverage of the data. The sample under study was drawn from the CALIFA survey and contains 300 galaxies observed with integral field spectroscopy. To study mean trends with overall galaxy properties, the individual radial profiles are stacked in seven bins of galaxy morphology (E, SO,Sa, Sb, Sbc, Sc, and Sd). The galaxies from the sample have decreasing-outward stellar extinction; all spirals show similar radial profiles, independent from the stellar mass, but redder than E and SO. Overall, we conclude that quenching processes act in manners that are independent of mass, while metallicity and galaxy structure are influenced by mass-dependent processes.