Spawn

Spawning refers to players and mobs being created and placed in the game world. Players will respawn on their spawn point upon death.

Spawn Point
When the world is generated, so is the player's spawn point. The player's first view of the map will be their spawn point by default (x=0,y=0,z=0). This location can be changed if the player digs four spaces downwards from it. However, this will only move the spawn point a few blocks away from the original position; it is not possible, using this method, to dramatically or controllably alter the location of the spawn point. It is possible to relocate the spawn point using a Map Editor. In Alpha, the initial spawn point is always on a sand block and facing east; relocated spawn points don't have to be on sand.

Players can locate their spawn point in game by using a compass.

In Multiplayer, the spawn point can be set by administrators and can even be a Spawn jail.

Mobs
Mobs spawn no closer than 24 blocks, in a 144 x 144 area around the player's location after a short delay. A player running through the game world will usually keep ahead of the waves of mobs spawning. Mobs are removed if they become more than four chunks away from the player.

Passive mobs
Passive mobs will spawn in grassy areas with a light level of more than 9.

Enemy Mobs
Enemy mobs can spawn on any block with a light level of less than 7, except Glass or Stone Slabs. They will not spawn if difficulty is set to 'Peaceful'. There are also Monster Spawners in dungeons that are a fixed spawn point for enemy mobs.

In The Nether, Ghast and Zombie Pigman spawning is independent of the light level.