There are four satellites capable of completely occulting the Sun: Io, Europa, Ganymede and Callisto.
Eclipses of the Sun from Jupiter are not particularly rare, since Jupiter is very large and its axial tilt (which is related to the plane of the orbits of its satellites) is relatively small—indeed, the vast majority of the orbits of all four of the objects capable of occulting the Sun will result in a solar occultation visible from somewhere on Jupiter, with every satellite except Callisto guaranteed to produce an eclipse on every orbit.
The related phenomenon of satellite eclipses in the shadow of Jupiter has been observed since the time of Giovanni Cassini and Ole Rømer in the mid Seventeenth Century.
Rømer correctly realized that the variations were caused by the varying distance between Earth and Jupiter as the two planets moved in their orbits around the Sun.
Later, in 1678, Christiaan Huygens used these errors to make the first accurate determination of the speed of light.