  We present the results of gravitational direct $N$-body simulations using the
Graphics Processing Unit (GPU) on a commercial NVIDIA GeForce 8800GTX designed
for gaming computers. The force evaluation of the $N$-body problem is
implemented in ``Compute Unified Device Architecture'' (CUDA) using the GPU to
speed-up the calculations. We tested the implementation on three different
$N$-body codes: two direct $N$-body integration codes, using the 4th order
predictor-corrector Hermite integrator with block time-steps, and one
Barnes-Hut treecode, which uses a 2nd order leapfrog integration scheme. The
integration of the equations of motions for all codes is performed on the host
CPU.
  We find that for $N > 512$ particles the GPU outperforms the GRAPE-6Af, if
some softening in the force calculation is accepted. Without softening and for
very small integration time steps the GRAPE still outperforms the GPU. We
conclude that modern GPUs offer an attractive alternative to GRAPE-6Af special
purpose hardware. Using the same time-step criterion, the total energy of the
$N$-body system was conserved better than to one in $10^6$ on the GPU, only
about an order of magnitude worse than obtained with GRAPE-6Af. For $N \apgt
10^5$ the 8800GTX outperforms the host CPU by a factor of about 100 and runs at
about the same speed as the GRAPE-6Af.
