We present Hubble Space Telescope blue spectra at intermediate spectral resolution for the nuclei of 23 nearby disk galaxies. These objects were selected to have nebular emission in their nuclei and span a range of emission-line classifications, as well as Hubble types. In this paper we focus on the stellar population as revealed by the continuum spectral energy distribution measured within the central 013 (~8 pc) of these galaxies. The data were modeled with linear combinations of single-age stellar population synthesis models. The large majority (~80%) of the surveyed nuclei have spectra whose features are consistent with a predominantly old (5 × 109 yr) stellar population. Approximately 25% of these nuclei show evidence of a component with age younger than 1 Gyr, with the incidence of these stars related to the nebular classification. Successful model fits imply an average reddening corresponding to AV ≈ 0.4 mag and a stellar metallicity of 1-2.5 Z☉. We discuss the implications of these results for understanding the star formation history in the environment of quiescent and active supermassive black holes. Our findings reinforce the picture wherein Seyfert nuclei and the majority of low-ionization nuclear emission-line regions are predominantly accretion-powered and suggest that much of the central star formation in H II nuclei is actually circumnuclear.