That is a great question! The reason why we can have a total eclipse of the Sun here on Earth is that the angular sizes of our Sun and Moon happen to be about the same, which allows the Moon to sometimes completely block out the disk of the Sun. The angular size of an object depends on both its size and distance from you. In order to have a total solar eclipse, you need a moon or other object whose angular size is about the same as the angular size of the Sun on whatever planet you are on. The orbital planes of the planet and the objects orbiting it also have to be in just the right configuration. If the angular size of the moon or other object, like an asteroid, is smaller than the angular size of the Sun, it will not block out the disk of the Sun if it passes across it. When an object whose angular size is much smaller than the angular size of the Sun passes across it, scientists call this a transit. As observed from Earth, we can also use telescopes to see transits of moons across the faces of the other planets. These kinds of transits might appear as eclipses to observers on the other planet.
The first observation of a transit or eclipse on another planet was made by the Mars rovers. You can read more here:
Scientists have observed transits of Pluto's moon Charon across Pluto, so this probably means that if you could go to Pluto, you could watch an eclipse from there. You can read more about eclipses on Pluto here:
The Hubble Space Telescope has also made observations of transits of Uranus' moon Ariel across the planet, which would appear as an eclipse to an observer located in Uranus' cloud tops. You can read more here:
Dr. Kris Sigsbee, University of Iowa