We report the first results from the evolution of generic black hole binaries, i.e., binaries containing unequal-mass black holes with misaligned spins. Our configuration, which has a mass ratio of 2 : 1, consists of an initially nonspinning hole orbiting a larger, rapidly spinning hole (specific spin a/m = 0.885), with the spin direction oriented -45° with respect to the orbital plane. We track the inspiral and merger for ~2 orbits and find that the remnant receives a substantial kick of 454 km s-1, more than twice as large as the maximum kick from nonspinning binaries. The remnant spin direction is flipped by 103° with respect to the initial spin direction of the larger hole. We performed a second run with antialigned spins, a/m = ±0.5 lying in the orbital plane that produces a kick of ~1830 km s-1 off the orbital plane. This value scales to nearly 4000 km s-1 for maximally spinning holes. Such a large recoil velocity opens up the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy.