We present ultraviolet (UV) photometry (near-UV (NUV) band, 180-280nm) of 405 asteroids observed serendipitously by GALEX from 2003 to 2012. All asteroids in this sample were detected by GALEX at least twice. Unambiguous visible-color-based taxonomic labels (C type versus S type) exist for 315 of these asteroids; of these, thermal-infrared-based diameters are available for 245. We derive NUV-V color using two independent models to predict the visual magnitude V at each NUV-detection epoch. Both V models produce NUV-V distributions in which the S types are redder than C types with more than 8{sigma} confidence. This confirms that the S types' redder spectral slopes in the visible remain redder than the C types' into the NUV, this redness being consistent with absorption by silica-containing rocks. The GALEX asteroid data confirm earlier results from the International Ultraviolet Explorer, which two decades ago produced the only other sizeable set of UV asteroid photometry. The GALEX-derived NUV-V data also agree with previously published Hubble Space Telescope (HST) UV observations of asteroids 21 Lutetia and 1 Ceres. Both the HST and GALEX data indicate that NUV band is less useful than u band for distinguishing subgroups within the greater population of visible-color-defined C types (notably, M types and G types).