Mob

Mobs are the various types of creatures and monsters found in Minecraft. Currently, there are twelve types of mobs. Each of these mobs are affected by the same environmental hazards as the player, including  burning and collision (falling) damage. Up to 200 hostile mobs and 15 neutral mobs can be on a map at a time. Mobs spawn no closer than 24 blocks and disappear if they are more than 4 chunks away from the  player.

The term "mob" is short for "mobile" and is pronounced as such. It has been used as a general term referring to any moving entities in games since the first MUDs surfaced.

Mob behaviour
Passive mobs will not attack the player and spawn only on grass panels with sufficient level of light (9 or greater).

Aggressive mobs will attack the player and spawn on every type of block with the exception of glass and half-blocks in a light level of 7 or  less. There are exceptions.

Since the Halloween Update, aggressive mobs can spawn in higher light levels than 7 depending on the depth above bedrock. For example, Mobs will spawn at level 14 light at depths of 16 and below, which means that torches are useless, and you would have to fill the entire place with Lava, Fire, Jack-O-Lanterns, Lightstone, or Sunlight to stop mobs from spawning. At level 8 and below, even those won't stop mobs from spawning.

The formula for the light required to stop mobs spawning at a certain depth is 16 - Layer (calculated from the bedrock) * 1 / 8, rounded down. So, at layer 64 mobs will spawn in level 8 light, and at layer 32 mobs will spawn in level 12 light. Higher layers, like 100, would require level 3 light.

Fish
Fish were added in the Halloween update. Fish are currently not visible, but are planned to be visible when you're swimming underwater in a future update. Fish are caught with the fishing rod and drop one raw fish which can then be cooked. TBA Alpha:
 * 1 piece of fish

Bats
Notch briefly mentioned coding bats, not much has been mentioned about them since.

Giants
Notch briefly ran a test of giant zombies during the very first version of survival, .31. (video)

It is possible Giants may become a future mob.

Dragons
Notch hinted during the Spider-riding skeleton update that he will add Dragons to the game. It is likely they will be classified as mega-mobs and will likely be found in caves underground or exposed to the surface. Dragons may also be able to fly or breathe fire.

Notch confirmed in his Twitter that he will definitely add a form of flying transportation. There is a chance that Dragons may be able to be ridden in a similar manner to pigs.

Prefix Mobs
Notch confirmed during the Brocraft.net stream that he will be adding 'prefix mobs'. This meaning that there will be mobs such as 'Burning Spider' 'Giant Zombie' 'Cobble Creeper' and etc. It's unknown how many prefixes there will be. A similar comparison could be that of the creatures from Borderlands or Dwarf Fortress.

Sea monsters
On July 21st, 2010, Notch commented via Minecast that Sea Monsters are a possibility. He particularly noted the possibility of sharks. Whales have recently been confirmed as a sea mob, although their purpose hasn't been specified.

Other Future Mobs
Notch has stated that wolves are going to be a definite addition, along with goblins who live in NPC Villages.

NPCs