The number of moons varies from planet to planet. While some planets do not have any moons, others have many moons. Also note that several moons in our solar system are yet to receive official confirmation, while the rest are confirmed moons (and have names).
Mercury has 0 moons.
Venus has 0 moons.
Earth has 1 moon and we call it the Moon.
Mars has 2 moons: Phobos and Deimos.
Jupiter has more moons than any other planet of the solar system. It has 67 moons, of which 53 are confirmed moons and 14 are awaiting official confirmation. Some of the famous moons of Jupiter include Io, Ganymede, Europa and Callisto.
Saturn has 62 moons, of which 53 are confirmed, while the remaining 9 are awaiting official confirmation. Titan is the most famous moon of Saturn.
Uranus has 27 moons.
Neptune has 14 moons, including one moon which has yet to receive official confirmation.
Pluto, which is no longer a planet, has 5 moons. Pluto is now considered a dwarf planet.
Ceres, another dwarf planet, has 0 moons.
Among other dwarf planets, Eris has 1 moon and Haumea has 2 moons.
Hope this helps.