Enderman

Endermen are unique neutral mobs that can teleport.

Spawning
Endermen spawn on solid blocks at light level 7 or less. They spawn commonly in the End, while in the Overworld they are rarer than most other mobs.

Endermen initially spawn in pairs.

Drops
Endermen may drop 0-1 ender pearls, and 5 experience when killed by a player or a tamed wolf.

Behavior
Endermen have a height of 3 blocks and are damaged by water and rain.

Endermen don't attack unless provoked by a player attacking them or looking at their bodies or upper legs from up to 64 blocks away. When provoked, endermen will open their mouths and shake with rage; when provoked by being stared at, they will also make a lengthy, loud, threatening sound and will not move until the player looks away or approaches too closely. If an aggravated enderman is hit by another mob, it will cease attacking the player.

They can also step up one full block without having to jump.

Endermen will continue chasing a player until they are either killed, sustain several hits, or become distracted by exterior elements like rain, fire, or sun; they are likely to teleport away to underground locations at day break.

Endermen can't be provoked by players looking through transparent blocks, from within a boat or minecart, or wearing a pumpkin on their head.

Endermen will be hostile towards endermites spawned by a player using ender pearls. Endermen will not attack endermites if a player is too close.

Teleportation
Endermen always attempt to teleport upon taking damage, such as from water. Most ordinary melee attacks are successful, but are followed by an immediate teleport (unless the player looks at the enderman's feet), usually to a few blocks behind the attacking player. Endermen cannot be attacked with projectiles in the PC version (including Splash potions of Harming), as they will always teleport away just before being hit. However in the Console Editions, it is possible to hit an enderman with a projectile by arcing a shot onto the enderman without placing the crosshairs on them directly.

When teleporting, endermen search for an air block within 32 blocks along each axis; if there is a solid block below that air block, they can teleport to it regardless of the downward distance. An enderman can teleport onto nearly any solid block, except blocks directly underneath water or lava or blocks with less than 3 vertical spaces above. Endermen will never teleport into water or lava.

An enderman cannot teleport when it is in a minecart, though in rain and water it will attempt to do so, always teleporting back into the minecart repeatedly until death.

Endermen will not teleport in the daytime while on soul sand unless they are damaged.

Moving blocks
Endermen have a unique ability to pick up certain block types (but not entities) and move them around. They will pick up blocks in a 4×4×3 region horizontally centered on the enderman and vertically at the same level as the enderman itself. They can pick up a block even if it is surrounded by other blocks. Endermen will not drop the block they are holding when enraged or killed.

Endermen can only pick up the following blocks:

When carrying a block, the enderman may randomly place it, in a 2×2×2 region horizontally centered on the enderman and vertically at the same level as the enderman itself, if the target location is air with a non-air block beneath and the block is allowed to be placed at the target location.

While endermen may breach walls, bridge fences, break redstone circuitry, and even construct golems by removing or placing blocks, such actions are entirely random and not purposeful.

One can summon an enderman holding any block using the {carried:Block ID} NBT tag.

Trivia

 * Notch claimed in public that the enderman is a "subtle" reference to "the Slenderman", a similar looking monster with a similar name. Given the later development of the End, it is possible he already had the name in mind, and did not choose it because of the Reddit thread in which their name was revealed.
 * In the Halloween texture pack for the Xbox 360 Edition, the enderman is re-skinned to look like the Slenderman.
 * Enderman sounds seem to be reverse audios:
 * the "idle1" sound is a reversed “here”
 * the "idle2" sound is a reversed "hiya"
 * the "idle3" sound is a down-pitched “whats up?” or "this way!"
 * the "idle4" sound is a down-pitched reversed "forever!"
 * the "idle5" sound is a reversed "uh oh!"
 * If a monster spawner is tweaked to spawn endermen, the model inside will have its head jutting out the top of the frame. In Pocket Edition, however, the model is shrunk to fit within the block.
 * The purple color of the particles that endermen emit are hard-coded into the game, so they cannot be re-colored without mods.
 * Amusingly, if an enderman is set on fire, they may try to put it out by teleporting into water, and therefore committing 'suicide', because they take damage from it. However they usually teleport back out, fresh and clean and ready to fight again.
 * Using spawn eggs, enderman continuously spawned into lava will humorously teleport - in the Nether, they will often teleport in circles for lack of room due to the lava oceans.
 * If you throw a splash potion of invisibility to an enderman, the enderman will be invisible, but you can still see the eyes. This is because the eyes, like spiders, are in a separate texture file.
 * In the End, an invisible enderman at a distance will become visible as a pale purple figure.
 * If you go to sleep in a bed it is possible for an enderman to teleport on it and knock you off. You will still continue to go to sleep as if you were in a bed.
 * Switching to spectator mode and taking an enderman's camera adds the invert shader, suggesting that they see The End as an island of blue cobblestone (because end stone is a yellowish inversion of cobblestone) in a white sky, with white pillars, white endermen with green eyes and a white ender dragon.
 * The collective noun for a group of endermen is "a haunting of Endermen", as stated by Dinnerbone.

Beta 1.8+
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