On Earth, we get snow, rain, fog, hail, and sleet, and all of them are basically the same thing: water. For a true change of weather, you need to go to other worlds. Here's a tour of what to expect on a trip through our solar system.
Mars: Dry Ice Snow
Scientists have known for years that the polar caps of Mars are made of a combination of water ice and dry ice (or frozen carbon dioxide—the same stuff that makes fog when you dump it into a pot of water). But how does it get there? The ice caps grow and recede with the seasons (in the Hubble images above, the carbon dioxide is receding with the onset of spring), so either the carbon dioxide is freezing directly out of the atmosphere, or it's snowing. Scientists working with data from Mars Reconnaissance Orbiter recently solved the puzzle: MRO detected clouds of carbon dioxide crystals, and clear evidence of snow falling out of them. The snow would not fall as flakes, but as tiny cuboctohedrons (which have eight triangular faces and six square faces). On the surface, Mars snow probably looks like granulated sugar.
Venus: Sulfuric Acid Rain
Io: Sulfur Dioxide Snow
Venus isn't the only hellhole in the solar system. Jupiter's moon Io would fit the bill pretty well, too. It's riddled with active volcanoes, covered in brimstone, and hiding a subsurface ocean of lava. And it snows the sort of snow you might get when Hell freezes over, because it too is made of brimstone: sulfur, and, more specifically, sulfur dioxide, which were detected when the Galileo orbiter flew through the volcanic plumes on its kamikaze mission in September 2003. Molten sulfur, heated to the boiling point below the surface of Io by torturous tidal flexing, sprays out of the volcanoes like a geyser would spray water on Earth. In the cold, airless void of space, the sulfur dioxide quickly crystalizes into tiny flakes; most of it falls back to the surface as a fluffy yellow snow. Galileo's sensors indicated that the particles were very small, perhaps 15-20 molecules apiece, so the snow would look extremely fine on the surface. In the photo above, the broad white semi circle of material is sulfur dioxide snow from a plume called Amirani.
Titan: Methane Rain
Titan is Saturn's largest moon, and the pictures revealed by Cassini and the Huygens lander show a world that looks surprisingly Earthlike, with riverbeds, lakes, and clouds. (The radar image above shows the shores of Kraken Mare, the largest known lake on Titan, with rivers flowing into it.) But this is deceptive. Titan is much colder: What looks like rock is water ice, and what looks like water is natural gas. A methane cycle (much like the water cycle on Earth) exists on Titan, driving seasonal rains that follow patterns (much like the ones tropical monsoons follow on Earth). When the season is right, the rain falls, filling vast but shallow basins bigger than our Great Lakes. As the seasons change, the lakes slowly evaporate. The vapor makes its way up into the atmosphere and condenses into clouds; the clouds drift to the other hemisphere as the weather shifts, and when the rain falls, it starts the next loop of the cycle.
Enceladus: Water and Ammonia Snow
Enceladus is one of the most active moons of Saturn. The south polar region especially is riddled with geysers that shoot water and ammonia hundreds of miles into space. Most of that leaves Enceladus altogether, forming Saturn's E ring. The rest falls back down, forming deep, powdery snow that would put the best "white smoke" of the Rockies to shame. But the snow falls very slowly. By mapping the snowdrifts, scientists have found that although the snow barely accumulates over the course of a year, the snow has been falling on some spots for tens of millions of years. Because of this, the snowpack is over 100 meters deep. And it's all light, fluffy snow; an unwary skier might disappear into the powder if he hit a particularly deep patch. This photo above shows Cairo Sulcus, a grooved feature in Encealdus' active south, its sharp edges softened by millenia of gentle snowfall.
Triton: Nitrogen and Methane Snow
Titan is cold enough to liquify methane, but Neptune's moon Triton is colder still. Voyager 2 discovered that Triton's surface is suspiciously new, and it's not just from volcanic resurfacing; the southern polar region also appears to be covered partially in a light, fluffy material that could only be snow. But while our snow is white and Io's snow is yellow, Triton's snow is pink. It's made of a mixture of nitrogen and methane. Like Io and Enceladus, the snow comes from geysers that blast liquid high up into space, where it freezes into fine particles that fall down as snow onto a terrain pockmarked by nitrogen/methane permafrost. Because of its color and the curious texture of the southern polar region, scientists call it "cantaloupe terrain."
Pluto: Nitrogen, Methane, and Carbon Monoxide Snow
Pluto has an awful lot in common with Triton, and apparently that includes snow. Although Pluto has never been seen close-up, careful observations with the Hubble Space Telescope suggest that it experiences snows of nitrogen, methane, and possibly carbon monoxide. Like Triton, this makes its surface very pinkish. Depending on the process that desposits it (geysers or frost or "diamond dust" snowfall, where the stuff just freezes straight out of the air and falls), this could be a fine powder or big, spiky piles of frost. We'll know more when NASA's New Horizons spacecraft visits; right now, it's about halfway there.
Jupiter: Liquid Helium Rain
The environments on gas giant planets are extreme in many ways; one is that there is a depth within them at which the atmospheric pressure is so great that exotic forms of matter appear, such as metallic helium and hydrogen. If the models are correct, above Jupiter's rocky core lies a deep ocean of liquid metallic hydrogen. Helium is a little harder to compress into a metallic form, so it doesn't mix with this ocean. It is heavier than hydrogen, though; scientists believe it falls through the metallic hydrogen ocean like droplets falling through the atmosphere, until it gets deep enough to become metallic.
Uranus and Neptune: Diamond Rain
Uranus and Neptune aren't really Jovian worlds; they're much colder than Jupiter or Saturn, and contain high fractions of water, leading some to call them ice giants. Another thing they contain is methane—lots of it, pressurized into a liquid state inside the giant planets. Methane is a hydrocarbon; under the right conditions (and models predict such conditions on Uranus and Neptune), the carbon within it can crystallize out as tiny diamonds. On Earth, "diamond dust" means superfine particles of ice suspended in the atmosphere on very cold days, but the phrase might be more literally true on Uranus and Neptune. The diamonds aren't accessible; they continually rain down towards the interior of the planets to be lost forever in a vast diamond ocean. Fans of Arthur C. Clarke may recognize this idea as part of the inspiration for "2061."
Bonus — The Sun: Plasma Rain
The Sun represents 99 percent of the mass in our solar system, so fittingly, it has what may be the most extreme precipitation in the solar system: plasma rain. Unlike the others on this list, you can actually see it from Earth. Huge loops of plasma are lifted up into space above the photosphere (what is generally considered the "surface" of the Sun) and suspended by magnetism, until finally something snaps and material is hurled violently into space in a coronal mass ejection. Not all of the material escapes, however; a lot of it falls back down as coronal rain. The video above, from June 7, 2011, was a particularly big and dramatic coronal mass ejection; look for the bright flashes as material impacts the photosphere.