Such systems revolve around their barycenter, the center of mass of the particles. If one particle is much more massive than the others, the barycenter will be very close to the massive particle, or even in it. Thus, the question becomes "why do stables systems have one particle that is so much more massive than the others."
If we look at N-body systems, we find that there are stable solutions for N=1 (lone particle) and N=2 (binary orbiting patterns), but at N=3 it starts to get tricky. The equations get chaotic and have a strong tendency to eventually eject one of the objects.
An exception to this rule is when one object's mass is so much higher than the others that you can basically ignore the effects of the other objects on it. For instance, the Earth's effect on the sun is pretty darn negligable, all things considered. This minimizes the chaotic effects which could cause ejection of objects.
So as such, you find systems with one particle (lone wolf), two particles (binary stars), or three or more particles with one substantially more massive particle (solar systems).
For a more formal handling of the topic, I recommend starting with the Wikipedia page on the Three Body Problem. It explains much of the difficulties and also points out some fascinating special cases that people have found over the years.