We analyze the u-r color distribution of 24,346 galaxies with M-r less than or equal to -18 and z<0.08, drawn from the Sloan Digital Sky Survey first data release, as a function of luminosity and environment. The color distribution is well fitted with two Gaussian distributions, which we use to divide the sample into a blue and red population. At fixed luminosity, the mean color of the blue ( red) distribution is nearly independent of environment, with a weakly significant (similar to 3 sigma) detection of a trend for colors to become redder by 0.1 - 0.14 (0.03 - 0.06) mag with a factor of similar to 100 increase in local density, as characterized by the surface density of galaxies within a +/- 1000 km s(-1) redshift slice. In contrast, at fixed luminosity the fraction of galaxies in the red distribution is a strong function of local density, increasing from similar to 10% - 30% of the population in the lowest density environments to similar to 70% at the highest densities. The strength of this trend is similar for both the brightest (-23 < M-r < -22) and faintest (-19 < M-r < -18) galaxies in our sample. The fraction of red galaxies within the virialized regions of clusters shows no significant dependence on velocity dispersion. Even at the lowest densities explored, a substantial population of red galaxies exists, which might be fossil groups. We propose that most star-forming galaxies today evolve at a rate that is determined primarily by their intrinsic properties and independent of their environment. Any environmentally triggered transformations from blue to red colors must occur either on a short timescale or preferentially at high redshift to preserve the simple Gaussian nature of the color distribution. The mechanism must be effective for both bright and faint galaxies.