Slime

A slime is a green, sentient translucent gelatinous cube that can appear in various sizes. They can splits into smaller slimes under certain conditions, and will follow the player around if they come close enough. With the exception of the smallest specimens, slimes will hurt the player upon contact. Slimes only appear in the bottom 16 (this is now disputed by Jeb's recent tweet ) layers of the map regardless of light levels or time of day, often in large caverns or open mines.

Uses
Each tiny slime yields 0 - 2 slimeballs upon death. Slimeballs are used to craft sticky pistons by combining it with a piston.

Slime Sizes
Slimes come in 4 sizes:
 * Tiny: 0.6 x 0.6
 * Small: 1.2 x 1.2
 * Big: 2.4 x 2.4
 * Huge: ? x ?

Only the tiny slimes drop Slimeballs. Slimes require Easy or higher difficulty levels to spawn.

Slime Spawning
Slimes only spawn in certain chunks that are determined pseudo-randomly by the seed of the world the player is in, and only below layer 16. (Though this is disputed by a tweet by Jeb where he suggests building caverns at height 20) Roughly 10% of all the chunks will be able to spawn slimes, based on the formula:

Random rnd = new Random(seed + (long) (xPosition * xPosition * 0x4c1906) + (long) (xPosition * 0x5ac0db) +             (long) (zPosition * zPosition) * 0x4307a7L + (long) (zPosition * 0x5f24f) ^ 0x3ad8025f); return rnd.nextInt(10) == 0

That is, Java's random number generator is first seeded by the number seed + (long) (xPosition * xPosition * 0x4c1906) + (long) (xPosition * 0x5ac0db) + (long) (zPosition * zPosition) * 0x4307a7L + (long) (zPosition * 0x5f24f) ^ 0x3ad8025f, then the random number generator is asked to generate its first random number between 0 to 9. If this number is equal to 0, the chunk coordinates (xPosition, zPosition) is able to spawn slimes. Multiplying the chunk coordinates by 16 will give the player coordinates since a chunk is 16x16.

Slimes only require a 1x1x1 space to spawn in and that the block below this space is opaque and the block above it is a transparent block or air. They can spawn in any light level and lighting does not affect its spawn rate. However, lighting up the surrounding area does decrease the chances of non-slime mobs spawning and thus indirectly increases slime spawning rates. In addition to this, slimes have 90% less chances of being picked for spawning compared to the other 4 hostile mobs (creeper/skeleton/spider/zombie).

Tiny slimes can spawn in Peaceful difficulty but all other sizes require Easy or harder difficulty settings. Slimes have equal chances to spawn at any size (and the selected size must be equal to Tiny for it to spawn on Peaceful difficulty). This means that if a slime that isn't the smallest size spawns in a 1x1x1 space, it will start to suffocate and split into smaller slimes. Slimes can spawn in spaces that already contain slimes.

Like any hostile mob, slimes will not spawn within 24 meters sphere radius of any player. Similarly, slimes will despawn after some time if no player is within 32 meters sphere radius of it, and despawn instantly if no player is within 128 meters sphere radius.

The slime spawning algorithm is explained in greater detail here: http://www.minecraftforum.net/topic/385523-slime-spawning/

An online tool to find slime spawning chunks (by providing the world seed and a search region to test for slime spawning) can be found here: http://www.minecraftforum.net/topic/397835-find-slime-spawning-chunks/ (See image on right.)

Via

Splitting Slimes
Larger slimes will split into 4 smaller slimes (that is one size smaller) if and only if the killing blow causes no overkill damage. This means that you can use a tool does the gcd of all the splittable slimes’ health, such as a bow, a wooden axe, a stone pick or a iron shovel (see: dealing damage), or simply by punching them. Drowning or suffocating slimes will also cause them to split on death.

Tiny slimes do not split and can be killed in any manner without regard for overkill damage as they will drop between 0 to 2 slimeballs on death. 1 huge slime is equivalent to 4 big slimes, 16 small slimes, or 64 tiny slimes for a total of 0 to 128 possible slimeballs.

Slimes of any size will burn upon contact with lava and die without splitting. Wolves attacking a slime will also not cause it to split.

Behavior
While huge, big, or small slimes will make a wet slapping noise, tiny slimes will make the same sound as a player walking on the block they are jumping on. Larger slimes will make a splattering sound distinct from their movement noises when damaging a player. Slimes do not grow larger or smaller over time.

While tiny slimes do not directly damage the player, they can easily push them into other hazards such as lava. These tiny slimes are sometimes kept as pets because they will follow the player around.

Slimes cannot swim and drown if they are completely submerged in water and will be unable to jump out. They do, however, have the ability to climb ladders and follow the player out of caverns.

History
Slimes were the fifth hostile mob added to the game on July 23, 2010 (Seecret Friday 6! Alpha 1.0.11). Notch limited slime spawning shortly afterwards because they would appear in abundance. A miscalculation in the new limit caused slimes to only spawn in strange locations, so Notch later completely disabled natural slime spawning.

Small slimes would drop 0 - 2 slimeballs in Beta. Notch confirmed in Coestar's livestream that slimes has been reskinned and returned in Beta 1.2_01 but were still very rare. Slimes became more common in Beta 1.3  A bug remedied in Beta 1.5 caused slimes to spawn in Peaceful mode and attack without any provocation. An SMP bug fixed in Beta 1.4 caused slimes that split to be visible only to the player that caused them to split and would not take any damage. Because these slimes were client-side, the player could only remove them by exiting and logging back into the server.

Trivia

 * The huge slime is the second largest mob in the game (only Ghasts are bigger), although if SMP plugins are used, slimes much bigger than Ghasts can be spawned.
 * Slimes are notorious for causing severe localized lag in multiplayer when they split into several smaller entities.
 * Slimes may have been inspired by a number of classic gaming monsters: Their shape and size resemble that of Gelatinous Cubes from Dungeons & Dragons (though admittedly that probably comes more from Minecraft's cubic art design than as a direct homage), and their splitting behavior resembles that of Zols from The Legend of Zelda and Puddings from Nethack. The name and the large, cartoonish face may be an homage to Yuji Horii's iconic Slimes from the Dragon Quest series.