  We present gravitational waveforms for the last orbits and merger of
black-hole-binary (BBH) systems along two branches of the BBH parameter space:
equal-mass binaries with equal non-precessing spins, and nonspinning
unequal-mass binaries. The waveforms are calculated from numerical solutions of
Einstein's equations for black-hole binaries that complete between six and ten
orbits before merger. Along the equal-mass spinning branch, the spin parameter
of each BH is $\chi_i = S_i/M_i^2 \in [-0.85,0.85]$, and along the unequal-mass
branch the mass ratio is $q =M_2/M_1 \in [1,4]$. We discuss the construction of
low-eccentricity puncture initial data for these cases, the properties of the
final merged BH, and compare the last 8-10 GW cycles up to $M\omega = 0.1$ with
the phase and amplitude predicted by standard post-Newtonian (PN) approximants.
As in previous studies, we find that the phase from the 3.5PN TaylorT4
approximant is most accurate for nonspinning binaries. For equal-mass spinning
binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN
order) gives the most robust performance, but it is possible to treat TaylorT4
in such a way that it gives the best accuracy for spins $\chi_i > -0.75$. When
high-order amplitude corrections are included, the PN amplitude of the
$(\ell=2,m=\pm2)$ modes is larger than the NR amplitude by between 2-4%.
