Slime

A slime is a green, sentient, gelatinous cube that can appear in various sizes and will follow the player around if they come close enough. The larger slimes can split into smaller ones under certain conditions and will hurt the player upon contact. Slimes only appear in the bottom 16 layers of the map regardless of light levels or time of day, often in large caverns or open mines.

Uses
A tiny slime will yield 0 - 2 slimeballs upon death. Slimeballs are a key ingredient of sticky pistons.

Behavior
While huge, big, and small slimes will make a wet slapping noise, tiny ones 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.

Unlike other hostile mobs, a slime will try to constantly path to the player if they are close enough, but when the player is far enough away, its movement becomes much slower, finally stopping when the player has exceeded the slime's awareness distance. In SMP, they path to the closest player and will only attempt to attack that player, ignoring other mobs and players even if attacked by them. Larger slimes are big enough to indirectly damage attacking wolves while attempting to attack a player. 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 completely submerged in water and unable to jump out. They will burn upon contact with lava and die with enough exposure. Despite the lack of any limbs, slimes can climb ladders and follow the player out of caverns.

Spawning
Slimes only spawn in certain chunks below layer 16 (an online tool to locate these can be found here). Tiny slimes will appear in Peaceful mode, but the larger ones will only appear in Easy and more difficult modes. To farm slimes, find a cavern or dig an artificial room near the bedrock level and keep it well-lit to discourage other hostile mobs from spawning.

For an in-depth explanation, see Slime/Spawning Conditions.

Splitting
Larger slimes will split into 4 slimes (all one size smaller) if and only if the killing blow causes no damage greater than the health of the original slime. This means that the player 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 punch the slimes. Drowning or suffocating slimes to death will also cause them to split or drop slimeballs, but slimes killed by lava or wolves will not.

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 then disabled natural slime spawning.

Small slimes started to drop 0 - 2 slimeballs in Beta. Notch confirmed in Coestar's livestream that slimes had 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 SMP plugins can be used to create much larger slimes.
 * 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.