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.

Mobs
Passive mobs

Passive mobs will not attack the player.

Neutral mob

Neutral mobs will not attack the player unless they are provoked.

Aggressive mobs

Aggressive mobs will attack the player.

Unused mobs

Unused mobs are mobs which are found in the source but are not at use.

Removed mobs

Removed mobs are mobs that once existed in the game but were later removed.

Prefixes
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.

Fish
In the halloween update, Notch was planning to add fish, however he had limited time and could only add the item fish and said in the future he will add the mob. In the files it can also be found that there is fish coding, but no model.

Giants
Notch briefly ran a test of giant zombies during the very first version of survival (video). It is possible Giants may become a future mob, although Giants are still hidden in the code and it is possible to spawn them with mods or a map editor.  File:OMG.jpg 

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.

Boss Monsters
There is a possibility of boss monsters for the players to slay.

Friendly/Hostile NPCs
Notch once mentioned having goblins settlements living in NPC Villages.

New Mobs
There are also hints that new mobs might be released in the far future. Below is the list of mobs that have been mentioned by Notch at least once and have a possibility of appearing in the game.
 * Bats - Notch briefly mentioned coding bats, not much has been mentioned about them since.
 * Dragons - Notch hinted during the Spider-riding skeleton update that he will add Dragons to the game. 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.
 * Wolves - Notch has stated that wolves are going to be a definite addition

Trivia

 * The Halloween Update version 1.2.0 allowed hostile mob to spawn in higher light levels at lower depths, using the formula 16 - (Layer ÷ 8). At level 8 and below, mobs could spawn even in sunlight. Notch reverted mob spawning to the original method in version 1.2.1, saying, "it was far too annoying. I have plans on what to do with this."

NPCs