An incredible discovery was made recently by the Curiosity rover on Mars, that was a bit overshadowed at the time by politics and other news. Smooth pebbles were found on an alluvial fan in Gale Crater. These pebbles are evidence of water flowing over the surface of Mars for extended periods of time.
(all photos here courtesy of NASA and JPL).
We've known for a long time that Mars has water ice on it and at one time almost certainly supported liquid water. It may have small, short-lived trickles of salty water in a few places even today. The pebbles show us something else, though. The pebbles, which appear to be scattered over a large alluvial fan, show us evidence of a river or stream on Mars that probably flowed for thousands or millions of years.
Above: more outcroppings containing water-deposited pebbles)
This doesn't mean there was continuous flow in this watercourse. Mars was likely drier than Earth even back then. The alluvial fan looks a lot like those found in very dry deserts on Earth such as Death Valley and the Atacama Desert:
In those deserts the dry washes can go years or even decades between seeing any surface flow of water. When it does come, though, the dry soils, exposed rock, and sparse vegetation mean that a thunderstorm can unleash massive flash floods. The same could have been true on Mars. We don't know of any vegetation that ever existed on Mars, so it's quite possible that the flash floods would have been even more severe than on Earth, though perhaps slower-moving due to the lower gravity. Then again, Mars could have also supported some tough, hardy life similar to that which occurs in Death Valley today. We won't ever know unless we find evidence of that life, because we can't disprove that it was there by NOT finding fossils or other evidence.
Dry washes prone to flash floods are not easy places to live, but the wash probably emptied into a lake similar to those in the Great Basin today. Perhaps it was a usually-dry lake like Amargosa Dry Lake in Death Valley or perhaps it contained significant amounts of salty water all the time, like Mono Lake in the Eastern Sierras.
Most washes in even the driest deserts also have a few spots of moisture. Upstream from the alluvial fan, in a steep gorge, often near a dry waterfall, there are places where bedrock forces the scant groundwater to the surface. On Earth, these little seeps are tiny islands of life in the desert, and often support a few weathered trees such as cottonwoods. The seeps are, of course, also vital to desert animals looking for water. Whether or not Mars ever held life, there apparently were dynamic watersheds, springs, ponds, rivers, canyons, flood plains, and other water features found all over Earth.
Water is an incredibly common compound throughout the universe, and with billions of planets (and countless moons around those planets too), there are certainly untold trillions of rivers flowing on other worlds. With all those planets it seems certain there must be other life out there too, maybe quite a bit of it.
One of the most bizarre recent findings from space is that rivers need not always contain water. On Titan, which is much, much colder than Earth but does support a thick atmosphere, there are many active rivers, but of methane, not water. Perhaps even more mind-bogglingly, the rock that these rivers erode through consists primarily of water ice!
The above air photo is from the Cassini-Huygens space probe.
A Google image search for Titan Rivers will bring up a vast number of incredible photos of river systems and lakes or oceans on Titan. Interestingly these images reveal a relatively young landscape - the rivers look to be young and very active, and few impact craters are evident. It seems that Titan in fact is covered in a very extensive network of tributaries and rivers, much like Earth. Unlike those on Mars, these are still very much active. And, they can't really be called watersheds - more accurately they are 'methanesheds'.
Conversely, there are probably very hot planets where rock flows in rivers as lava, through some other substance, and water exists only as a gas? Venus is very hot and may experience some sort of drizzle, but no evidence of 'watersheds' created by other flowing liquids.
We are surrounded by incredible wonder and diversity in our universe, but the fact remains that despite all these rivers on other worlds, we are utterly dependent on our own rivers and water for our survival. We are, of course, all on one tiny planet amidst all this wonder, and for the time being unable to leave. Even if we do, Earth will always be 'home'. We need to take care of our rivers.