As of March 2012, we know of 67 moons around Jupiter.
Jupiter has at least 67 known moons. The largest four are called Io, Europa, Ganymede and Callisto. These four moons are called the Galilean satellites because they were first seen in 1610 by the astronomer Galileo Galilei. Ganymede is the largest moon in the solar system, with a diameter of 3,260 miles. Io has a lot of active volcanoes and is covered with sulfer. Callisto may have a water ocean beneath its heavily cratered icy, rocky surface. Europa, which is covered by a cracked, icy surface, may also have a liquid water ocean. The other moons are smaller and have irregular shapes. Most of these small moons are thought to be asteroids which were caught by Jupiter’s strong gravity.
The four largest moons are Io, Europa, Ganymede and Callisto, and can be seen through binoculars if you have good eyesight. They were discovered by Galileo through his primitive telescope in 1610, and the fact that they were visibly orbiting Jupiter was an important part of his argument that the Earth is not at the center of the Universe.