One big difference between a lunar eclipse and a solar eclipse is that you don't need to be in any special place on Earth to see it. If you can see the Moon anywhere in the sky, you'll see the eclipse.
Are eclipses seen on other planets?
Yes, all you need is a moon large enough to block out the Sun. If you could visit Jupiter, you'd see some of the best and clearest eclipses in the solar system caused by its moons.