  Coalescing binary black hole mergers are expected to be the strongest
gravitational wave sources for ground-based interferometers, such as the LIGO,
VIRGO, and GEO600, as well as the space-based interferometer LISA. Until
recently it has been impossible to reliably derive the predictions of General
Relativity for the final merger stage, which takes place in the strong-field
regime. Recent progress in numerical relativity simulations is, however,
revolutionizing our understanding of these systems. We examine here the
specific case of merging equal-mass Schwarzschild black holes in detail,
presenting new simulations in which the black holes start in the late inspiral
stage on orbits with very low eccentricity and evolve for ~1200M through ~7
orbits before merging. We study the accuracy and consistency of our simulations
and the resulting gravitational waveforms, which encompass ~14 cycles before
merger, and highlight the importance of using frequency (rather than time) to
set the physical reference when comparing models. Matching our results to PN
calculations for the earlier parts of the inspiral provides a combined waveform
with less than half a cycle of accumulated phase error through the entire
coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs)
for iLIGO, adLIGO, and LISA, highlighting the contributions from the
late-inspiral and merger-ringdown parts of the waveform which can now be
simulated numerically. Contour plots of SNR as a function of z and M show that
adLIGO can achieve SNR >~ 10 for some intermediate-mass binary black holes
(IMBBHs) out to z ~ 1, and that LISA can see massive binary black holes (MBBHs)
in the range 3x10^4 <~ M/M_Sun <~ 10^7 at SNR > 100 out to the earliest epochs
of structure formation at z > 15.
