Everybody remembers Pluto's demotion to dwarf planet in 2006. This reclassification was triggered by the discovery of Eris, an object far out beyond Pluto's orbit that was found to be 27% more massive than Pluto. So either it had to be the tenth planet, or Pluto shouldn't classify as planer either.
In addition to these two dwarf planets there are currently known to be three more. Two other trans-Neptunian objects (that is, objects beyond Neptune's orbit) are Haumea and Makemake. That leaves only one dwarf planed residing inside the orbit of the farthest (known) planet in the solar system.
Ceres, located between Mars and Jupiter was also declared as a planed when it was found in 1801. At the time it was the seventh planet as Pluto nor Neptune hadn't been found yet. It was however reclassified as an asteroid after more smaller objects were found around the same orbit which we nowadays know as the asteroid belt.
In addition to our own moon, there are 6 other moons bigger than these dwarf planets in our solar system. After the reclassification there is now only one planet left that is smaller than any of those moons: Mercury.