Peter Ward and Donald Brownlee, in their book Rare Earth, note that not only does our earth possess physical properties that may well make it unique in all the universe, our moon is quite special as well. It's not only rare in terms of its size relative to its planet, but it is absolutely essential in a number of ways to the existence of higher life forms on earth.
A large moon with strong gravitational pull is necessary to keep the earth's axial angle stable. If the earth's axis wobbled, as it would if it had no large moon to offset the gravitational tugs of other planets, the earth would experience enormous climatic variations which would make the evolution of higher life forms quite improbable. Moreover, the moon at its formation, pulled away from the earth many of the noxious gases that formed the early atmosphere. If the moon did not exist, for example, the earth would have retained an atmosphere high in CO2 causing a runaway greenhouse effect which would make the earth as uninhabitable as Venus.
A large moon also causes significant lunar tides which enrich the seas with nutrients and help make them more than vast biological deserts. The gravitational influence of our moon also slows the rate of earth's rotation allowing the atmosphere to be placid enough to permit life to emerge on the earth. Finally, a large moon protects the earth from meteorites from elsewhere in the solar system by drawing many of them toward itself.
Guillermo Gonzalez notes in Privileged Planet that the size of the moon is precisely what it needs to be to permit a total eclipse of the sun which allows for the study of the sun's atmosphere. This single fact has been responsible for much of the advance of scientific knowledge over the centuries. The precise fit of moon and sun during a total eclipse allowed early geometric calculations of the size and distance of celestial objects. It also allowed scientists to determine the nature of the sun's composition which has enabled them to determine much about the size and composition of other stars in our galaxy and other galaxies in the universe, including the fact that those celestial objects are rapidly receding from us and that the universe is expanding. This knowledge has enabled us to infer an initial Big Bang origin to the universe, and much else.
All of this simply because the moon is the size it is and the distance it is from the earth.
The moon was believed to be formed in a collision with a Mars-size object which impacted the earth early in its development. This collision probably melted the earth's crust and allowed surface iron to sink toward the core of the planet. This enabled the earth to develop a protective magnetic field and, by removing much of the iron from the surface where it would have bound up any oxygen in the vicinity, it permitted the atmosphere to become oxygenated.
If the material that formed the moon had taken a reverse orbit after this primordial impact, it would have decayed and fallen back to earth. If the impact had occured at a later stage in the earth's development the earth would have been too massive to allow as much material to be ejected, and the resulting moon would have been smaller and less effective.
Remarkably, in other words, this impact had to occur at just the right time, at just the right angle, with just the right force, by an impactor of just the right size and momentum, at just the right spot for a moon of just the right size to form.
What amazing coincidences nature and chance are capable of!