The highly anisotropic distribution and apparent alignment of the Galactic satellites in polar great planes begs the question of how common such distributions are. The satellite system of M31 is the only nearby system for which we currently have sufficiently accurate distances to study the three-dimensional satellite distribution. We present the spatial distribution of the 15 currently known M31 companions in a coordinate system centered on M31 and aligned with its disk. Through a detailed statistical analysis we show that the full satellite sample describes a plane that is inclined by -56° with respect to the poles of M31 and has an rms height of 100 kpc. At 88% the statistical significance of this plane is low, and it is unlikely to have a physical meaning. We note that the great stellar stream found near Andromeda is inclined to this plane by 7°. Most of the M31 satellites are found within <±40° of M31's disk; i.e., there is little evidence for a Holmberg effect. If we confine our analysis to early-type dwarfs, we find a best-fit polar plane within 5°-7° from the pole of M31. This polar great plane has a statistical significance of 99.7% and includes all dSphs (except for And II), M32, NGC 147, and PegDIG. The rms distance of these galaxies from the polar plane is 16 kpc. The nearby spiral M33 has a distance of only ~3 kpc from this plane, which points toward the M81 group. We discuss the anisotropic distribution of M31's early-type companions in the framework of three scenarios, namely, as remnants of the breakup of a larger progenitor, as a tracer of a prolate dark matter halo, and as a tracer of collapse along large-scale filaments. The first scenario requires that the breakup must have occurred at very early times and that the dwarfs continued to form stars thereafter to account for their stellar population content and luminosity-metallicity relation. The third scenario seems to be plausible, especially when considering the apparent alignment of our potential satellite filament with several nearby groups. The current data do not permit us to rule out any of the scenarios. Orbit information is needed to test the physical reality of the polar plane and of the different scenarios in more detail.