Satellites and binary systems seem to be common in the gravitational accretion processes that produce stars, planets and satellites.

Binary stars are the rule, not the exception. Over half of all stars are known to be members of binary systems, and triple, quadruple and even higher level hierarchies are not uncommon. Since many binaries are extremely difficult to detect, binaries may be even more common than we know and it is likely that solitary stars, like our sun, are quite rare. Even the sun might be considered a sort of binary, since Jupiter is close to the arbitrary boundary between star and planet.

Of the eight major planets in our system, 6 have at least one satellite and many minor planets and Kuiper belt objects have companions. Galaxies often have satellite galaxies, and many seem to be orbited by clouds of globular clusters.

Satellites seem to be a normal part of the mechanism that allows objects to condense from flat, rotating clouds of orbital debris. And the process appears to be hierarchical. Although none of the satellites of planets and planetoids in our solar system have their own satellites (probably due to the gravitational perturbations present in the crowded cis-solar environment) among stars there does seem to be a hierarchy: binary stars are often orbited by other stars or binary pairs, and pairs of pairs and so on. I read somewhere that one star has eleven known companions! Any theory that describes the process of planetary formation has to be able to explain this.

Some binaries are very close, with the stars actually in physical contact with each other. Many others are distant, with the members so far apart that only the most subtle and indirect methods can reveal their binary nature. How the distances between binary members is variable, that is, how the distances are distributed in stellar populations, and how that distribution may (or may not) be related to the mass ratio of the two members has (as far as I know) never been properly investigated. This may be due to the fact that many binaries are difficult to detect, so we don't have enough data to make proper comparisons, but these new orbital observatories make that possible now.

Many orbital configurations are dynamically possible, but don't seem to exist in nature, either because they inherently unstable or simply because Nature doesn't like them. And the orbital resonances one sees, like the Kirkwood Gaps and the Pluto-Neptune Coupling seem to emerge from this chaos almost unexpectedly (although why they do so seems obvious once you actually see it happening!). Its funny how something as simple and straightforward as Newton's Law of Gravity can manifest itself in so many subtle, complex and surprising ways...