We describe a new survey for unbound hypervelocity stars (HVSs), stars traveling with such extreme velocities that dynamical ejection from a massive black hole is their most likely origin. We investigate the possible contribution of unbound runaway stars, and show that the physical properties of binaries constrain low mass runaways to bound velocities. We measure radial velocities for HVS candidates with the colors of early A-type and late B-type stars. We report the discovery of 6 unbound HVSs with velocities and distances exceeding the conservative escape velocity estimate of Kenyon and collaborators. We additionally report 4 possibly unbound HVSs with velocities and distances exceeding the lower escape velocity estimate of Xue and collaborators. These discoveries increase the number of unbound HVSs by 60% - 100%. Other survey objects include 19 newly identified z 2.4 quasars. One of the HVSs may be a horizontal branch star, consistent with the number of evolved HVSs predicted by Galactic center ejection models. Finding more evolved HVSs will one day allow a probe of the low-mass regime of HVSs and will constrain the mass function of stars in the Galactic center.