When unequal-mass black holes merge, the final black hole receives a kick due to the asymmetric loss of linear momentum in the gravitational radiation emitted during the merger. The magnitude of this kick has important astrophysical consequences. Recent breakthroughs in numerical relativity allow us to perform the largest parameter study undertaken to date in numerical simulations of binary black-hole inspirals. We study nonspinning black-hole binaries with mass ratios from q=M1/M2=1 to q=0.25 (eta=q/(1+q)2 from 0.25 to 0.16). We accurately calculate the velocity of the kick to within 6%, and the final spin of the black holes to within 2%. A maximum kick of 175.2+/-11 km s(-1) is achieved for eta=0.195+/-0.005.