Water

Water is a fluid that can only be placed by the player when using a bucket. On newly-generated maps, water is common at ocean level (elevation 63) in the form of lakes. It also appears in pools, (and in Indev, Infdev, Alpha, and Beta springs) underground and lakes above ground.

Though it cannot be placed by the player in single-player Creative, it could briefly be placed in Survival by detonating a Creeper in water and collecting 'water blocks'. It can be placed in Infdev, Alpha and Beta by using a bucket. There was also a Water-generating block in Indev mode, but has since been removed in newly-generated maps. However, they can still be placed in a map editor such as Omen.

The texture for water was changed in the 0.0.19a client update (June 20, 2009), adding animation.

Water cannot be found in The Nether and water from a bucket will evaporate as soon as it touches anything in there.

Water reduces light by 2 for every block, in addition to normal dispersion.

Spreading
In Creative mode, Water spreads horizontally and downwards by duplicating itself to empty squares. Water spreads faster than the speed of a walking player, and if left alone covers everything at or below the level the water started at if there is a direct connection. Water is transparent and slows down the player if it is moving through it. Water cannot spread within a five-by-five area of Sponge (two blocks on each side and diagonally, with the sponge at its center); this enables it to be cleaned up quickly using sponges.

In Survival mode, Water is much deeper and the player starts to drown after your 15-second air gauge is eliminated. Water cushions fall damage to a certain extent, in the same way that it dampens horizontal movement as well. You still can die from it, however. It is advised that you allow at least two, or three blocks of water for any unreasonable jump.

In Indev, Infdev, Alpha, or Beta mode, Water spreads across surfaces in a slightly more realistic way but cannot spread on top of another Water block. This allows the creation of waterfalls in these modes. The player can pick up Water blocks from sources such as an ocean or a lake by use of a Bucket. When placed again, the Water creates a spring which generates flowing or falling water. When a spring is destroyed, all flowing water created from will slowly dry up. If there is a hole six or less blocks away, the water will tend to flow in that direction. Spawner blocks and falling water that has landed on a solid block will always flow in at least one direction unless restricted. Water will travel a distance of 7 tiles with the counter resetting every time it lands on a lower level. If a block next to a water spawner block is destroyed, the water will immediately flow in that direction unless there was a block beneath the destroyed block.

Management
Water tends to be harder to deal with on non-creative modes.

Placing a block in the same space as water will replace the water. Entire lakes can be filled this way. Some Decorations, Ladders and Sugar Cane will also displace water.

Using a redstone wire, a one-block water flow can be redirected by supplying power to the source block, which will cause it to reset the flow towards the now-nearest terrain depression. This is further elaborated in this thread. It however cannot be reversed.

This re-calculation is made because redstone wire when toggled changes the block from redstone(on), to redstone(off). whenever a block updates on any side of water, the water re-calculates where to flow, but does not cut off its current direction of flow.

Springs
In Infdev mode, springs can consist of either Water or Lava. Springs are randomly generated in caverns underground and sometimes above ground. Springs can also be placed by the player by picking up Water from the ocean by use of a bucket and then placing the Water again. A spring will generate Water which cannot flood a room because Water cannot spread on the top of another Water block. If a spring is removed, all Water that was created from it will also be removed, which makes it hard for things to be ruined by springs.

Infinite Spring Duplication
In Infdev, Alpha, and Beta, Water springs can be duplicated using any basin of at least three empty spaces, as long as the bottom is not Water, Glass, Ice, a Monster Spawner, single Stone Slab, Stairs, Ladders, and other non-solid blocks. Placing a Water spring at two sides of an empty space will create a water spring in the empty space. Also, removing the water from the middle of the basin will allow adjacent water springs to generate a new spring. (This does not work with lava.)

This can also be done in a 2x2x1 pit with two buckets of water dumped in opposite corners. Using this method, it does not matter where you take the water from. It will replenish itself regardless, even if one of the original source blocks of water is scooped up.

Source blocks cannot be duplicated over an area deeper than 1 block.

Water Elevators
In Classic, water can be held into a column by using a sponge. This can be used to make pillars of water, which can be used as elevators.

In Infdev, Alpha and Beta, "standing" halfway off of a falling/floating water tile prevents damage from drowning.

Water ladder
Used to facilitate quick climbing in a strictly vertical manner. The accessible portion of this structure is a 1x1 shaft, but if created above ground would require 3x3 blocks of horizontal space.

Base Jumping
Water can be used to jump off of buildings and structures that would otherwise kill you by building a pool to land into. The water must be a minimum of 3 blocks deep (which is recommended because the highest number of block you can fall off of without hurting yourself is 3, thus allowing you to safely exit the pool). This can be used along with water elevators to enter and exit a very deep mineshaft or cave in a matter of seconds, saving time, and also saving the wood and stone otherwise used to make ladders and steps. It is recommended that you make a fairly wide pool in case you hit the edge and die.

Water Brake
Alternatively, you can create a floating "water brake", using water held in mid-air with signs or other non-solid blocks that resist water. Two or three blocks above the bottom of your vertical mineshaft, place a sign to support the water block, then place the water block above the sign. The way this works is that when the player collides with the water, it reverts the falling distance to zero and slows the player's downward velocity dramatically. The player can then safely land on the solid floor in a 2 block high air pocket under the water without taking fall damage or having to swim.

Warning: Water brakes should use signs instead of ladders as falling players can hit the edge of a ladder and die.

Water Bucket
Water can be collected by right clicking on a water block with a bucket, giving a water bucket. However only water spring/source blocks can be collected, not shallow flowing water.

Trivia

 * Zombies and Skeletons can survive daylight if they are in water.
 * Sometimes, water forms a small cascade in the middle of the ocean while creating the map. Rare glitches can even create big cascades which changes sea level. (trees in water will be able to spawn)

Wasser