How often are there lunar eclipses on Jupiter For the Earth-Moon system, the orbit of the Moon is at a slight incline compared to the plane of the ecliptic. This incline is enough for there to be eclipses roughly twice a year rather than every lunar month. 

But Jupiter is much bigger, so its shadow is bigger also. So it seems more likely for a satellite to go into its shadow. How often does this happen?
Every Galilean moon and inner moon go into lunar eclipse once per orbit.

How often is there a lunar eclipse of the Jovian moons?

I set up a little animation of the Galilean moons (I didn't include the inner moons), and made a few assumptions (negligible moon size, sun at infinity, perfectly circular orbits) and found that there is a lunar eclipse in the Jovian system just under 10% of the time.



Here's a bigger version of the second graph.