Jupiter was known to have 16+11 = 27 moons, where the last 11 were discovered in 2001! see here for details. Most interesting about the new moons is that a few area actually retrograde in their orbits---they orbit opposite to Jupiter's spin. This has implications as to how they got there. From the site: "Essentially the only plausible way to produce irregular satellites is by capture. However, it is not easy for Jupiter (or any other planet) to directly capture passing asteroids from heliocentric orbit. In general, some of the initial energy of the heliocentric objects must be dissipated so that Jupiter can hold on to them. The origin of the dissipation that lead to the capture of Jupiter's irregular satellites is unknown. In fact, at the present time there is no plausible source of dissipation so that capturing satellites is presently almost impossible. It is theorized, however, that the youthful Jupiter sustained a bloated atmosphere that extended far above the cloud tops of the present planet. Friction with this atmosphere could have captured the irregular satellites."
By far the largest and best known are the 4 Galilean Moons, so named because they were discovered by Galileo. Indeed, the 4 Galilean moons are not difficult to see from Earth with even small telescopes. The adjacent image (Ref) shows a Voyager montage of the Galilean moons.