We report the discovery of eight new Milky Way companions in ~1,800 deg^2 of optical imaging data collected during the first year of the Dark Energy Survey (DES). Each system is identified as a statistically significant over-density of individual stars consistent with the expected isochrone and luminosity function of an old and metal-poor stellar population. The objects span a wide range of absolute magnitudes (M_V from -2.2 mag to -7.4 mag), physical sizes (10 pc to 170 pc), and heliocentric distances (30 kpc to 330 kpc). Based on the low surface brightnesses, large physical sizes, and/or large Galactocentric distances of these objects, several are likely to be new ultra-faint satellite galaxies of the Milky Way and/or Magellanic Clouds. We introduce a likelihood-based algorithm to search for and characterize stellar over-densities, as well as identify stars with high satellite membership probabilities. We also present completeness estimates for detecting ultra-faint galaxies of varying luminosities, sizes, and heliocentric distances in the first-year DES data. Show Partial Abstract