The only edits I would make to Kay T's answer is Saturn, which has 60 (known) moons, Uranus has 27, and Neptune has 13. It is likely all of the gas giants have even more than what we currently know about.
Mercury and Venus do not have moons.
Earth - 1 (the Moon or Luna)
Mars - 2, Deimos and Phobos
Jupiter - 63. The largest are Io, Europa, Ganymede, and Callisto.
Saturn - 18 plus 6 small satellites discovered by the Cassini probe.
Uranus - 21
Neptune - 8
Pluto (now a dwarf planet, sub-category plutoid) - 3, Charon, Nix, and Hydra