Tectonic processes move or distort a planet's surface. Earth's plate tectonics has crustal plates floating on the mantle. Tectonic processes on other planets and moons in our solar system occur to varying degrees, but none have plate tectonics as on Earth.
Moon and Mercury
Impact craters form when meteors crash into the surface. When the solar system was young there was lots of debris to impact planets. With less debris, fewer impact craters now form. Hence planets or moons with few impact craters have had significant tectonic activity. Worlds saturated with impact craters have had little tectonic activity reshaping their surfaces.
Both Mercury and Earth's Moon have many impact craters, so their tectonic activity has been limited. These small worlds cooled quickly. (Think about a spoonful of coffee cooling faster than the larger cup.) Cool planetary interiors lack the heat needed to power tectonic activity.
The lunar maria, which are large smooth areas, formed from tectonic activity billions of years ago. Large impacts from space formed large basins which filled in as lava oozed from the interior. The Moon also has rilles which were once lava rivers. Hadley's rille is the best known.
Mercury has no maria, but billions of years ago lava flows formed intercrater plains. Mercury also has cliffs, called scarps, that are hundreds of kilometers long. Scarps may have formed when Mercury's crust shrank and buckled as its interior cooled.
Venus
The geology of Venus shows considerable tectonic activity. Venus has about 1600 large volcanoes, and perhaps hundreds of thousands of smaller volcanic features. About 80% of the surface is covered with solidified lava flows. The larger volcanoes are often shield volcanoes, similar to Earth's, which form from lava flowing up through the volcano's center.
Venus has many smaller volcanoes called pancake or dome volcanoes. Venus also has very large volcanic features called coronae. Both these volcanic structures form when lava flows up from the mantle and swells the crust.
Astronomers do not know if Venus still has active volcanoes because thick clouds obscure the surface. However geologic evidence suggests that tectonic activity shaped the surface of Venus as recently as a few hundred million years ago.
On Venus tectonic activity moves the crust vertically rather than horizontally as on Earth.
Mars
Tectonic features on Mars are the largest in the solar system. Olympus Mons and the Tharsis Ridge volcanoes dwarf Earth's volcanic mountains and are the largest known. Olympus Mons extends up to 700 kilometers at its base and towers for about 27 kilometers (almost 88,000 feet) above the surrounding Martian surface. Huge!
Valles Marineris is a canyon on Mars that is deeper than the Grand Canyon and long enough to reach across the United States.
Mars is no longer geologically active. The lack of moving plates on Mars causes its impressive geology. After dormant periods, Martian volcanoes erupt at the same spot forming large volcanic mountains. On Earth the crust drifts during dormant periods forming a chain of smaller mountains.
Jupiter's Moons
The Galileo mission observed about 60 active volcanoes on Jupiter's closest large moon, Io. Io does not have tectonic plates so the volcanoes are randomly distributed. Europa, Jupiter's second major moon, has an icy crust surrounding a water mantle. The icy crust has many cracks exhibiting an unusual type of tectonic activity.
Tidal forces from nearby Jupiter supply the heat needed to cause tectonic activity on these moons.
Studying tectonic activity on other moons and planets helps geophysicists fully understand Earth's tectonic activity.
Further Reading
Hester, Jeff et al. 21st Century Astronomy. WW Norton, 2002.