In Minecraft, the many creatures both friendly and fierce that populate the world are known as Mobs (short for mobiles) and they come in a range of different sizes and types.
These are categorized in several categories depending on their role, and then listed in alphabetical order.
Playable
These are you!
The Player
This is you. The person you play as. (The only way to encounter one besides yourself is in Multiplayer.) Who are you? Well, that's up to you. The skin of The Player is entirely customisable, and there are many different ways your character can look. On a Multiplayer server, you can help and/or hurt many other Players in their tasks. For more info, see the 'Controls' section.
The player can jump only one block high, and only has ten hearts worth of health which can be easily depleted by a lurking Creeper. However, their ability to build, mine and craft gives them the highest potential of any mob in the game - so it's a good thing you are them!
When they die, they drop their inventory and some of their experience orbs.
Passive
These creatures are, obviously, passive to what you do. No matter how much you hit them, they aren't going to actually attack you. This category includes farm animals, squids and villagers.
Chicken
The chicken will occasionally lay eggs that you can collect.
Cow
An empty bucket right-clicked on this will fill the bucket with milk, which cures poison, removes potion effects & can be used for making cake. (or am I LYING???? nah, jk)
Mooshroom
With all the properties of a cow, this hybrid can also be milked with a bowl to get mushroom stew and sheared with shears to get red mushrooms (but turning it into a cow).
Pig
These are pink, little, cow-shaped animals that act weird because they don't play in the mud, either because Mojang didn't intend for there to be mud or they don't have very impressive AI.
Sheep
Drops raw mutton and wool. Use shears to get more wool than by killing. Wool grows back after eating grass.
Squid
Drops ink sac. Spawns in water. Suffocates outside water.
Villager
Neutral
These creatures are Neutral, as in they won't attack you... unless you provoke them. For the Enderman, just looking at them will bother them, but the Zombie Pigmen are nice enough to leave you alone until you start beating them up.
Enderman
Endermen are tall characters who shares lots of similarities with Slenderman. If you do as much as look at them with your curser, they will scream and warp behind you. Endermen are also very strong and hard to defeat. when they are dead, they will drop ender pearls. Ender pearls are essential for completing the game.
Zombie Pigman
Hostile
These guys are angry and mean. If they see you, they will come towards you and attack. Be ready to fight them or find somewhere to run or hide.
Blaze
Drops blaze powder.
Creeper
Drops gunpowder. Explodes.
Ghast
Drops ghast tears. Flying enemies ho shoot exploding projectiles.
Magma Cube
Drops magma cream
Silverfish
Skeleton
Drops arrows and bones. Fires arrows.
Slime
Drops slimeballs
Spider
Drops string
Cave Spider
Spider Jockey
A skeleton riding a spider.
Zombie
Tameable
These creatures may run, or stand around, or attack you if you make them mad, or do many other behaviors, but you can coax them out of that if you do the right sequence of events to tame them - then they can follow you around as pets!
Ocelot
Tame with raw fish. Scares creepers off. Takes no fall damage.
Wolf
Tame with bones. Collar can be dyed a different color. Attacks enemies you attack.
Utility
These creatures are built. You may have to stack some snow or iron blocks in certain manners to build them, and then they will help you if you know what you are doing.
Iron Golem
Use 4 iron blocks in a T-shape. Put pumpkin on center blocks. Great defense against mobs.
Snow Golem
Stack two snow blocks and put a pumpkin on top. Trows snowballs at enemies. Leaves a layer of snow behind.
Bosses
The big guys. These creatures will take a while to take down, have their own health bars, and have very special strategies for defeating them.
Ender Dragon
Wither
Unused
Unused mobs are in the game, but they do not spawn naturally - you will have to use external programs to spawn them.
Giant
Removed
These creatures used to be in the game, before they were removed. Now their data doesn't exist in Minecraft.
Human
Rana
Steve
Black Steve
Beast Boy
Unimplemented
These mobs will be added in future Minecraft updates.