As of 2020, how many planets, including dwarf planets, are known to exist in the solar system?

There are 8 planets, or 13 planets, if you count dwarf planets, in the Solar system. They are Mercury, Venus, Earth, Mars, Ceres, Jupiter, Saturn, Neptune, Uranus, Pluto, Eris, Haumea, and Makemake. Of those, Ceres, Pluto, Eris, Haumea, and Makemake are considered dwarfs.

Four other planetary objects have been put forward as possible dwarf planets, but as of the time of this writing, they are not recognized. They are Quaoar, Sedna, Orcus and Gonggong.

To classify as a full planet, the planetary object must "clear the neighborhood around their orbits". A dwarf planet is a planetary object that is not a moon, but has not cleared its orbit - that is, the orbital path contains smaller planetesimals (asteroids, etc) that have not been consumed by the planet, or forced into other orbits due to gravity.