Our data has improved considerably in the last 20 years.

Mercury: no moons

Venus: no moons

Earth: 1 moon

Mars: 2 moons, Phobos, Deimos

Jupiter: 67 moons, some of which do not yet have proper names. The most famous are the Galilean moons, Io, Europa, Ganymede and Callisto.

Saturn: 62 moons, some of which do not yet have proper names. The most famous, by far, is Titan, which is significantly more massive than any other Saturnian moon.

Uranus: 27 moons, all of which are named after characters in the works of Shakespeare and Alexander Pope. Five are well known; Titania, Oberon, Miranda, Ariel, Umbriel

Neptune: 14 moons, the most massive by far being Triton.

While Pluto, Eris, Haumea, Orcus and Quaoar are considered dwarf planets, they nevertheless have moons.

Pluto: 5 moons, Charon, Nix, Hydra, Kerberos, Styx

Eris: 1 moon, Dysnomia

Haumea: 2 moons, Hi'iaka, Namaka

Orcus: 1 moon, Vanth

Quaoar: 1 moon, Weywot

Moons are the natural satellites of a planet. A number of planets of our solar system have moons, while a few do not. The number of moons of each planet in our solar system are listed here for easy reference: 

• Mercury: 0
• Venus: 0
• Earth: 1
• Mars: 2
• Jupiter: 67
• Saturn: 62
• Uranus: 27
• Neptune: 14

Pluto, which is technically no longer a planet, has 5 moons. 

As one can see, Jupiter has the largest number of moons, followed by Saturn. In comparison, Mercury and Venus do no have any moons at all and we on Earth have only 1 moon.

Also note that several of these celestial bodies have already been confirmed as moons, while some are awaiting confirmation. For example, out of the 67 moons of Jupiter, 17 are awaiting official confirmation. Similarly, 9 moons of Saturn are awaiting official confirmation.

Hope this helps.