Main article: Geography
Erosion occurs when on a planet or moon there is some fluid flowing over surface. The fluid can be a gas, can be a liquid or can be a soft solid.
Erosion occurs in many place all over the Solar System and for sure it occurs in other systems. The best example of erosion is planet Earth, which is modeled by water. Mars also shows signs of water erosion and it is clear that in past there were rivers flowing on its surface. Titan shows rivers made of methane and dunes made by winds. Incredibly, even Pluto sows signs of erosion, but in this case it is made by flowing glaciers and it looks similar to glacier valleys found on Earth. The most surprising was Vesta which is a small asteroid and shows limited signs of erosion and sedimentation by flowing water. It looks like even Venus has some sort of valleys.
There are large celestial bodies without signs of erosion, but all of them share something in common: the lack of an atmosphere. The Galilean moons and the large moons of Saturn (except Titan), all show no signs of erosion.
Now, let's analyze the data we have so far:
- Mercury has no signs of erosion. What is known as Great Valley is in fact caused by tectonic activity and shows that Mercury is shrinking in size .
- Venus has valleys, one of them with the length of Nile River. It looks like these valleys are created by flowing lava. Since Venus's ground temperature is much higher then Earth's, lava needs much more time to cool down .
- Earth has many signs of erosion, made by wind, by liquids (water) and by solids (glacier). We know about their existence very well.
- Luna seems to have a few valleys  that are of volcanic origin.
- Mars has a global and complex networks of valleys, which most of sure were created by river erosion .
- Among the asteroids, since they have no atmosphere, erosion is very rare, but still it has been detected:
- Vesta has very short valleys around a few crater rims. They are caused by subsurface ice that melted after a meteoric impact . However, affected terrain is less then 1% of the surface.
- Ceres shows landslides that are similar with avalanches and moving glaciers . However, they cover a very small surface.
- Io shows existence of lava valleys , but they cover only a small surface.
- Europa has a subsurface ocean that acts like a mantle, while the surface ice works like a rocky crust. However, without a significant atmosphere, there is no direct force working above the surface.
- Ganymede shows existence of a few valleys and lava flows . However, the valleys are in fact of tectonic origins and lava is in fact water that solidifies. The whole crust is made of dirty water ice.
- Callisto shows nothing but craters . There are small valley-like structures on crater walls, but they were not made by flowing fluids.
- Titan shows rivers  created by flowing methane and dunes  created by winds.
- Tethys has a canyon named Ithaca Chasma, but it is of tectonic origin. Just like Tethys, all Saturnian moons except Titan show no signs of surface erosion.
- The moons of Uranus and Neptune are not well explored. The only moon with a significant atmosphere is Triton. All other moons are not expected to have significant forms of surface erosion.
- Pluto shocked the world with its unusual features. It has glacier valleys  in many places and of different sizes.
If we look at all this data, we can conclude that surface erosion occurs wherever there is something flowing on the surface. In some cases, erosion processes affect most of the surface of a planet, while in others, it is limited to small areas. Erosion occurs even in places we wouldn't expect, like on an asteroid, but it is very limited. Also, volcanism can bring fluids to the surface.
Depending on what causes the erosion process, it can be local or global.
Global erosion processes: On Earth, Mars and Titan, erosion is of a global scale. The valleys existing there are made to handle large rivers. We can conclude that if there is a dense atmosphere and if the planet has or had a liquid to flow on its surface, erosion will be global.
Extended but not global: Venus has a less developed valley system, but could still support future rivers to form. An explanation could be the fact that valleys on Venus are created by molten lava. If they were created by flowing water, it happened before Venus undergone a runaway greenhouse effect and the amount of water was small or did not have enough time to create a global network of valleys. A different scenario happens on Pluto, where erosion is caused by methane, nitrogen and carbon monoxide glaciers. Glacier valleys are not connected into a global network. In fact, they are maintained by glaciers located on high mountains or by ices sublimated around Sputnik Planitia. Pluto has not enough volatile ices to cover its entire surface. And even if it had, glaciers don't flow like liquids, they flow much slower and cannot travel such long distances as liquids to form a global network of canals.
If erosion occurs, all matter that is carried away will be deposited somewhere else. The process of sedimentation is seen at the end of each valley, be it made by a flowing liquid or by glaciers. In case of wind erosion, sedimentation occurs near the same place under the form of dunes.
Importance in terraforming Edit
Geography of a planet dictates its hydrology and its climate. If a planet has valleys, it will be far more easy to terraform then if it hasn't. Technicians will not need to create artificial valleys for future rivers, by using heavy machinery, by controlled explosions or by a Noah Flood. Rivers will start to flow just where they did before. However, if the network of valleys is limited, we will have to continue nature's work.
Unfortunately, in case of an Outer Planet, where usually the crust is made of water ice, during terraforming, the ice will melt and all former Geographic features will be erased. But still, in case of rocky planets, existing valleys will be very useful.