1. Flowing liquid water on Mars ↑
In September 2015, NASA announced that they've found evidence of liquid water currently flowing on Mars[1].
This began with the discovery of dark streaks on the sides of several craters[2]. These are up to a few hundred meters long, and appear seasonally. They form when it's ‘warm', at over -10 °C, and disappear when it is colder. These were found using the HiRISE (High Resolution Imaging Science Experiment) camera attached to NASA's Mars Reconnaissance Orbiter (MRO) spacecraft.
A team led by Lujendra Ojha found hydrated salts in these regions using data from the MRO's CRIS (Compact Reconnaissance Imaging Spectrometer)[3]. These salts are only present when the streaks are, and so it's thought that the streaks must be caused by flowing salt water.

Animation of flowing water in the Hale Crater on Mars, an image created using data from NASA's Mars Reconnaissance Orbiter spacecraft. Image credit: JPLraw/Public domain.
Over 25 spacecraft have been to Mars since the 1960s. Evidence for water on Mars was first found by NASA's Mariner 9, which launched in 1971. Data from Mariner 9 showed that Mars had once contained rivers, which had led to the formation of large, complex canyons. Data from NASA's Viking 1 and Viking 2, which launched in 1975, showed that Mars once contained both rain and oceans.
Data from NASA's Mars Global Surveyor and Mars Pathfinder, indicated that Mars may have once have been warm and wet, with flowing water, and NASA's Mars Odyssey orbiter found evidence of frozen water on the Martian surface.
The European Space Agency's (ESA) Mars Express confirmed the presence of frozen water and carbon dioxide at the Martian poles, and NASA's Opportunity rover found rocks that are thought to have once been underwater in a salty sea.
There are a number of landers and orbiters currently on Mars, and many new missions to Mars are in progress. But Mars is not the only place outside of Earth to contain water.
Water is very common in the universe because hydrogen and oxygen are both reactive and abundant. Hydrogen is the most common element in the universe and was created in the big bang, and oxygen is a fairly common element made inside of stars.
2. Water elsewhere in the Solar System ↑
Water has been found in trace amounts on many moons, and on every planet in the Solar System[4a][5]. Frozen water exists at the bottom of deep craters on Mercury's poles[6] and on the Moon[7]. Venus is thought to have once contained oceans[8], and it's thought that oceans currently exist below the frozen surface of at least three of Jupiter's moons, at least two of Saturn's moons, and possibly on Neptune's moon Triton. There may also be subsurface oceans on dwarf planets Ceres and Pluto[4b].
The majority of water in the Solar System resides in comets, which orbit the Sun from the Kuiper belt and the Oort cloud. The Kuiper belt is thought to be composed of about a trillion comets[9], and the Oort cloud may contain up to 2 trillion[10]. In total, these may contain tens of thousands of times the amount of water in the Earth's oceans*.
Amino acids – the ‘building blocks of life' – have also been found inside comets, and it's possible that both water and amino acids were transported to Earth and other planets when they were bombarded with comets during the formation of the Solar System[11].
Further evidence of liquid water in the Jupiter system may come from NASA's Juno spacecraft, which lunched in 2011, and will arrive at Jupiter in 2017. Juno will look for water in Jupiter's atmosphere. The ESA plan to launch a mission to Jupiter's moons, Ganymede, Callisto, and Europa, in 2022. All of these moons are thought to contain oceans. This mission is known as Jupiter Icy Moon Explorer (JUICE), and should arrive at Jupiter in 2030. NASA also plans to launch a mission to Jupiter's moons in the 2020s, known as the Europa Clipper. This will focus on looking for evidence of life on Europa.
Further evidence of liquid water in the Saturn system may come from the Cassini spacecraft, which launched in 1997, and is currently in orbit around Saturn. Data from the Cassini spacecraft, and its lander, the Huygens probe, have already shown that water exists on two of Saturn's moons, Titan and Enceladus. Titan was found to have sand dunes, coastlines, islands, and mountains, and Enceladus was found to erupt in geysers that can send water into orbit around Saturn. In September 2015, data from Cassini was used to show that Enceladus might also contain a global ocean[12] that could be suitable for life[13].
Evidence of water in the Kuiper belt may come from NASA's New Horizons mission. New Horizons passed Pluto in July 2015. Scientists were surprised to discover that it may contain liquid water, and we'll know more about why this is as information is transmitted back to Earth. It's hoped that the New Horizons spacecraft will be able to give us similar information about at least one more Kuiper belt object.
3. Water outside of the Solar System ↑
Water has also been observed outside of the Solar System, in molecular clouds[14], protoplanetary discs[15], exocomets[16], and in the atmospheres of exoplanets[17].

Artist's impression of the TW Hydrae system, a protoplanetary disc that contains ‘oceans of water'. Image credit: NASA/JPL-Caltech/Public domain.
Scientists are most interested in looking for liquid water, as this is thought to be essential for the formation of life. For liquid water to exist on a planet, it must be far enough away from its star so that the water doesn't boil away, but close enough that it doesn't freeze. This area is known as the habitable zone, and it's currently thought that there could be tens of billions of planets in the Milky Way that exist within the habitable zone[18].
At least 30 have already been identified[19], including ‘water world' GJ 1214b[20]. There are numerous missions that may provide further evidence of water outside of the Solar System.
We are beginning to discover that water is everywhere in the universe, and where there is water, there may be life.

Sardu Reef. Image credit: Alex Ries, 2012/Copyrighted, used with permission.
* ↑ | Total mass of water in a comet = 1013 kg. Total mass of water in Earth's oceans = 1.4×1021 kg. Total mass of water in a comet × number of comets = 1013 × 3×1012 = 3×1025 kg. Water in cometsWater in the oceans = 3×1025 kg1.4×1021 kg = 21,429. |
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UPDATE: As of 2017, 52 exoplanets have been discovered within the habitable zone. In 2016, astronomers at the University of California, Santa Cruz found evidence of clouds of water around the brown dwarf WISE 0855. Brown dwarfs are objects that are much larger than planets, but are slightly too small to become stars.