The internet is abuzz with the new evidence of the possible ninth planet in our Solar System. With those nine objects, the asteroid belt, the Kuiper belt, and everything else in our Solar System - the number of objects which orbit our star is pretty massive. Is this odd for a star its size? It's known that our Sun is a comparatively small star, so does having so many planets make it an oddity? Or do larger stars tend to have dozens or planets, even hundreds?
From an exoplanet-finding point of view, the Sun has between one and three planets.
The major exoplanet-finding techniques in current use involve watching for either periodic Doppler shifts as the planet's gravitational pull causes the star to wobble, or periodic brightness shifts as the planet transits the star. Both require that the planet is large enough and close enough to generate a measurable signal and that the orbital period is short enough to let astronomers distinguish periodic variations from one-off variations; the transit method additionally requires that the planet's orbit crosses the star from the point of view of Earth (which favors close-in orbits). Looking at the Solar System with these techniques:
- Mercury: too small
- Venus: Maybe visible
- Earth: Maybe visible
- Mars: too small
- Jupiter: Highly visible
- Saturn: Orbital period too long
- Uranus: Orbital period too long
- Neptune: Orbital period too long
- "Planet 9": Orbital period too long
If you look at this graph of exoplanet discoveries, Jupiter is solidly in the cluster of blue Doppler discoveries, Saturn is just past the "we've been watching for one full orbit" right-hand edge of that cluster, Earth and Venus are somewhat below the sloped minimum-period-mass line, and everything else is nowhere near the detection range.
The reason the Sun has far more known planets than any other star is simply because we've got a better look at it.
We can't detect whether there are or are not objects of similar "small" sizes orbiting other stars. We simply lack that level of ability. From a scientific point of view I'd simply say "don't know". From a practical point of view I would expect other stars to have systems with a huge variety of things in orbit - there's no reason not to expect this, but it's bad science to assume it.
Given that Kepler has detected stars with 5 or 6 planets that exist in an extremely flattened plane and much flatter than the solar system, then we can be reasonably sure that stars with more than 4 planets are reasonably common.
Given the many mechanisms for scrambling the orbital inclinations out of a perfectly flat configuration, and that seeing multiple transiting planets around a star becomes impossible even if their inclinations are a little different (e.g. only one planet could be seen to regularly transit our Sun if observed from another star), then it is likely that many if not most of the exoplanet systems we detect have more planets than are currently known.
In other words, the fact that we see some multiple transiting systems, despite them being inherently geometrically improbable, means that there must be lots of multiple planetary systems.