Rain is an element in the game. Much like snowfall, it is a type of weather. It currently exists in Classic, Beta and full versions of the game.
Rain in Classic: Rain is a feature activated by pressing F5 in-game in Classic. Rain can also fall on Multiplayer, but cannot be seen by other players. It will only fall where the sky isn't blocked and has no effect on gameplay. Rain is a single moving sprite. When it falls on a block it makes a splashing effect. To improve frame rate, rain isn't replicated all throughout a map. It is instead one sprite on all sides of the player. When the player goes inside and far away from the falling rain it disappears but reappears when you move close to outside again. Water does not stop rain like a solid block. Instead, it falls through as if there was air. The same applies to lava and small plants. Rain in Classic does not decrease the light level. 
Rain in Beta and Full: Rain and falling snow were included in Beta 1.5. Rain looks identical to the rain in Classic, but also plays two different sound files. 
Precipitation varies by biome. Rain never falls in deserts though the sky still darkens, and in winter biomes snow falls instead of rain. If you are between a biome that produces rain and another that produces snow, you can see both snow and rain. 
Effects:
Rain and Snow: Rain and snow Rain and snowfall are temporary but global occurrences.[1] 
During rain and snow, thunderstorms become possible. 
Rain and snowfalls decrease the light level by 3, to light level 12 in full daylight. Thunderstorms decrease light level to 7 in full daylight, which allows hostile mobs to spawn aboveground.[2] 
Rain: Rain and snow Rain and snowfall are temporary but global occurrences.[1] 
During rain and snow, thunderstorms become possible. 
Rain and snowfalls decrease the light level by 3, to light level 12 in full daylight. Thunderstorms decrease light level to 7 in full daylight, which allows hostile mobs to spawn aboveground.[2] 
History: In early Classic, rain was introduced to the game to test out this feature. It was purely for cosmetic purposes at that time. The mechanics were simple, only testing if there is a block above to shelter the rain. It could be toggled on and off in-game using the F5 key. This feature later vanished when Indev was introduced. 
After Minecraft Beta 1.5's announcement, a preview video was uploaded onto the TeamMojang YouTube channel showing weather and other future updates. Rain was then introduced the following week. 
Bugs: When going down a ladder exposed to the sky, rain moves slower than it should, and moves at the same pace as if one were normally falling. This makes the rain appear to freeze and the player fall faster than it. In the opinion of some players, this looks really cool. This effect can also be achieved by pressing shift to descend while flying in Creative mode. 
If you are in a cloud, the rain will let you "see" through the cloud. 
When you open your inventory, the sun, moon and stars re-appear. 
If you start to break glass with rain in front of it, the rain will disappear. 
Rain doesn't pass through signs. 
Rain does not extinguish burning mobs when they are standing in doorways. 
In the 1.8 Pre Release, rain can sometimes fall through blocks, such as stone and dirt. This includes Grass. 
Rain can also fall through wooden plank blocks. 
Rain can fall through Jack-O-Lanterns and Pumpkins. 
Rain falls on rivers, even if you are in a desert. 
In some areas (especially in extreme hills biomes), the rain to ground collision effect isn't attached to the rain, which also means the rain sound doesn't play while it is raining. 
Flying above the clouds in Creative Mode allows you to see that the rain doesn't come from the clouds themselves, but from the sky above them. 
Trivia: Rain is a single moving sprite. 
In minecraft 1.0.0 (minecraft release) if you turn particles to minimal then rain wont make any sound. 
Rain falls only in the two middle lines of a block, therefore it looks like it is not raining directly above you, but actually the "square" in the sky is shifted half a block in each direction. 
In the code snow and rain are classified the same. 
Although you cannot see the sun during rain, the glow associated with sunrise and sunset is still visible. 
When the player uses a Bed, the rain stops when they wake up. 
Rain still falls above the clouds. Notch's explanation is that the gray above the clouds during a storm is another layer of clouds and the origin of the rain.[7] 
An Enderman will start to burn to death if it is raining 
Rain only moves with you, but it appears enemies far away, such as Endermen, are affected. 
Although you cannot see the rain sprite in the desert; if it is raining and you are at the edge of the biome, you can still see particles bouncing off the grass or stone in the neighboring biome. 
In some very rare occasions, it appears to be raining in caves. This will only happen if the cave almost, "Touches the Skybox". 
Rain actually falls one block into the void (Layer -1). This can be achieved by digging a vertical shaft down in Creative mode, removing the bottom layers of Bedrock and floating inside the Void (in flying mode). Note that no particles are emitted from the rain, due to the absence of a block below it. 