Each type of mob in Minecraft has a certain AI (Artificial Intelligence) system with different behaviors and mechanics. Passive mobs will flee in random directions after being hurt, while hostile mobs will face and chase/attack the Player as soon as they come close. Neutral mobs will remain neutral until a player or mob attacks it, at which point the neutral mob will turn hostile toward and attack the entity that hit it.
 All mobs
All mobs randomly walk around. When they come to a 1 block high wall, they jump. They avoid falling 4 or more blocks (falling 4 or more blocks means taking fall damage). They all float in water except for slimes, magma cubes, and iron golems, which sink. (Although in future updates, slimes and magma cubes can swim.)
 Farm animals
Chickens, cows, pigs, mooshrooms, and sheep, are attracted to light, grass, or wheat (carrots for pigs and seeds for chickens) that is carried by The Player. If two animals of the same species are fed wheat (or carrots or seeds) within five minutes of each other, they will walk towards each other into a "kiss" to spawn a baby animal of the same species. If an animal is damaged, it will sprint in random directions. Animals avoid lava and falls of more than one block. Farming Animals will wander into water if in their path and will always swim upwards to the top of the fluid, even if a block is blocking air.
 Pig being ridden by a player
If the player is holding a carrot on a stick, the pig moves in the direction that the player faces. The pig gradually speeds up until it moves at 5 blocks per second. It will stop responding to the player if it touches water. The pig will slightly speed up when the player right-clicks.
Adult villagers will 'socialize'. This is modeled by a pair of villagers moving to face one another or the player at a distance of about a meter, as if they were talking. Sometimes larger groups will form in this way. Child villagers 'socialize' in the same way as the adults, and will also sprint around the village, seemingly playing tag. All villagers will attempt to enter houses when it is raining or at night, and will also flee from zombies. Note that identifying a 'house' is a challenge for a computer AI, and this may give rise to unexpected villager behavior.
Villagers will neither attack nor flee if the player attacks them, but if their village is large enough to have spawned an Iron Golem it may arrive to protect them. Villagers will also interact with the golem: when they see one, they stop and stare at it. The golem may in turn offer them a poppy. When an Iron Golem offers children a poppy, they will approach slowly and run away as soon as they have the poppy.
Villagers try to live in 'houses', and they use the number of available houses as a cue for whether or not to breed. To a villager, a house is a wooden door which has more blocks with direct sky light on one side of it than on the other. An acceptable 'house' for a villager does not require any form of lighting nor walls. Also, the floor material of the house is not relevant, and does not even need to exist.
It is possible to build very many seemingly reasonable house-like structures that the Minecraft AI cannot recognize as houses, and it's also possible to build structures which do count as 'houses' despite being parred down to the very minimum.
Note that because a 'house' needs a door, and zombies in Hard mode can destroy doors, after a zombie attack even the surviving villagers may stop recognizing their former residences as houses and become lost when they wander off into the wilderness. Although, if the complete structure of a 'house' is destroyed except the door, previous residents will still congregate on the 'inside' of the lone door, but newly spawned villagers will not recognize the lone door as a house.
Other important notes: A villager cannot find a house unless the door of the house (regardless of structure) is within 15 blocks. While actively occupying a 'house' (as to escape rain or such), villagers will stay within 3 blocks of the door and will not wander throughout the structure. Villagers will try to squeeze as many of themselves as possible into a single 'house' if it is the nearest to them.
Bats are the only passive mob in Minecraft that fly, and the only flying mob in the overworld. Bats spawn in caves, where the light level is 10 or less (higher than for hostile mobs, which is 7 or less) and hang upside-down during the day. At night or when approached by the Player, bats will take off and fly around randomly. All bats will attempt to enter a cave when daylight approaches, although they are not affected by daylight.
Squid spawn in water and swim in it. If they're not in water, they don't move. Their tentacles always move, even if they're not in water. If they are not in water they will suffocate and die within a few seconds.
Ocelots sprint away from a player if the player is close, unless the player is still. When a player holds raw fish, the ocelot slowly moves closer. Ocelots can hunt chickens.
 Tamed cat
Tamed cats follow its owner, and if it's near its owner, it will wander within 8 blocks of its owner. Tamed cats will teleport to its owner if more than 16 blocks from its owner if it's standing. Unlike wolves, cats don't attack. Tamed cats will often sit on chests. Tamed cats also tend to "scare" creepers, they however do not kill them.
Wolves are neutral mobs that spawn in forest and taiga biomes. Wolves live in packs of up to ten wolves that will attack sheep naturally. They will wander around in the pack and ignore you, but if you attack one, all the wolves in the vicinity will turn hostile and attack you. You must then either kill the wolves or let them despawn. They will not attack cows, pigs, chickens, or mooshrooms. They will shake when getting out of water. Wolves only despawn when hostile to a player.
 Tamed wolf
Tamed wolves follow its owner, and if it's near its owner, it will wander within 8 blocks of its owner. Tamed wolves will teleport to its owner if more than 16 blocks from its owner if it's standing. It will attack any mob or player that its owner attacks. It will also attack any mob or player that attacks its owner. Note: Wolves will not attack creepers.
Endermen are neutral mobs that spawn in the End and the Overworld. They will pick up blocks and carry them around, eventually replacing them somewhere else. This block handling is random, that is they will not purposely tear down your wall, but may "accidentally" breach your defences (perhaps by placing a block that lets monsters cross a fence or wall). They are passive at first, but turn hostile if you put the crosshairs in between its eyes or on its torso. Only then, will the enderman become hostile. Unlike wolves and zombie pigmen, endermen near it will stay neutral. It will become neutral if it touches water. It teleports when it touches water, when you look at it's face or chest while it is attacking you, sometimes when it attacks you, if it's in sunlight, or if it is hit with a projectile. In daylight, Endermen will become peaceful and will teleport away if stared at or attacked.
 Zombie Pigman
Zombie Pigmen are undead neutral mobs that roam around the Nether in packs of 4, no more, no less. Some packs will combine making it seem like one giant pack. Wielding golden swords, they are peaceful at first, but when attacked, all of them in the area attack you, like wolves. They cannot be killed by fire. They move faster than zombies when provoked. Some zombie pigmen can pick up items, making it dangerous to drop your sword. Note: They will run blindly towards you when provoked, making no attempt to ignore holes, cliffs, or obstacles such as cacti.
 Iron Golem
Iron golems are found in villages, can be created by the player, and move slowly. They also have a LOT of health, can kill you in one unarmoured hit, and can generally be quite the formidable foe if you aggravate them! Iron golems attack hostile and neutral mobs except for creepers and can attack players if; attacked by the player (except the person who created it), a player attacks a villager nearby (works only if you didn't create the Iron Golem), or if the player has a bad reputation in the village that the iron golem is in, being hostile to that player only. Iron Golems sometimes offer villagers a rose (as of 1.7.2, roses no longer exist and the Iron Golems offer villagers poppies instead).
Before 1.0, zombies, creepers and skeletons ignored everything except their target, once they had been aggravated by the player or another entity, leaving them vulnerable to environmental dangers such as lava pits and sudden cliffs. The mobs would charge blindly forward instead of attempting to avoid said hazards. This allowed for the creation of simple pitfall traps. As of 12w37a, hostile mobs are now more "fearless" in Hard difficulty, meaning they are willing to drop from higher falls.
Zombies attack by moving relatively slowly towards a player or a villager, and will damage them on contact. They do not try to avoid being hit, and will continue to pursue the player even when being counter-attacked. If they encounter a door they will bang loudly on it, but they can only actually break through a wooden door on the Hard difficulty setting or in hardcore mode. They cannot break through iron doors. In hard mode, their habit of attacking doors makes them a significant threat to villagers, as after a few days of attacks they can destroy every door in a village, leaving the villagers 'homeless' and highly vulnerable. (See the Villager AI description for further details.) Also, they slow down for a few seconds when hit. They are healed by damage potions and damaged by health potions. Some zombies can pick up items if the gamerule "mobGriefing" is set to true.
 Before 1.2
Zombies, Skeletons, and Creepers made no attempt to avoid cliffs or other obstacles, and would simply try to jump over anything in their path.
 1.2 AI overhaul
Zombies and skeletons will attempt to find and run to the cover of nearby trees or caves, or enter bodies of water to protect themselves from burning up during the day. They also try to avoid 4+ block holes and lava where possible. If the player is on the same level as the Mob, with a hole in between, the Mob will go around the hole if possible.
Skeletons will circle the player with a constant radius while attacking in an attempt to evade attacks. They are healed by damage potions and damaged by health potions. They will also shoot other skeletons if hostile towards them.
 Before 1.2
The presence of a skeleton is identifiable by the soft rattling sound of its bones. It will walk and jump around aimlessly until it spots the player. At that point, it will start firing arrows in the player's direction with moderate accuracy, aiming at head level when it is at full health and at torso level when injured. When approaching a target, a skeleton will move to its left just before it fires an arrow. It will also run, making itself more difficult to hit. However, these tendencies often get skeletons stuck in small alcoves and lava.
Their arrows travel in a straight line after Beta 1.8, however, prior to Beta 1.8 their arrows used to travel to in a wide arc, which would sometimes cause the arrows to get stuck in the ceiling. If skeletons were in a 2 block high area, they could almost never hit you unless they were very close, or if their health was low, and they were shooting from their torso.
 1.2 AI overhaul
Skeletons received a similar AI update to the Zombie AI update. As with zombies, skeletons also attempt to seek out the cover of nearby trees or caves, or enter bodies of water to protect themselves from burning up during the day. Skeletons will also follow the player around obstacles should the player try to hide from the skeleton. For example, a skeleton spots the player and the player attempts to hide around a corner of a wall. The skeleton will seek out the player and attack once they found them. Similar to creepers, skeletons now avoid falls if they can. It is a rare occurrence but you can find skeletons riding spiders. This rare mob is called a Spider Jockey. This is of course only if the spider spawned with the skeleton on it. While riding the spider, the skeleton loses his ability to circle strafe, but gains speed to get into the fight quickly, to stay on the players heels should the player attempt to flee and the skeleton can now travel over walls. If the skeleton is killed, then the spider will remain alive, forcing the player to choose between targets. Some skeletons can pick up items, which makes it dangerous for you to drop your weapon. If you happen to encounter a skeleton, drop your weapon, and the skeleton picks it up, you need to kill the skeleton in order to get your weapon back. Once you get your weapon back, it'll look like it's been used.
 Wither Skeleton
Wither Skeletons charge at you instead of shooting at you because they hold a sword. If a normal skeleton manages to pick up a sword, it will do this too. If you get hit by a wither skeleton, you get the Wither potion effect. If they are given a bow, they will no longer charge at you and instead behave like normal skeletons. Additionally, the arrows they shoot will be on fire, as if the bow had the Flame enchantment.
Spiders run at the same speed as the player, and attack by leaping at you. If encountered in light levels of 9 or higher, they don't try to attack you unless you attack them. However, a spider that spots you in a light level less than 9 and then ventures into a light level 9 or higher will remain hostile (This is why hostile spiders may be found in the morning close to where the player has spent the night). Spiders can see through and climb walls. This will often leave them pushing against the ceiling of an adjacent cavern in a vain attempt to reach the player if spawned nearby underground. Since they're 2 blocks wide, they can't fit through doorways, though this won't stop them from trying.
 Cave Spider
In addition to what is mentioned in the "spider" section, cave spiders are smaller, and they poison their target, but only in normal mode or harder. Note that being smaller it can fit through smaller spaces as well, such as slabs and 1x1 passageways.
Creepers will silently approach any player they see, attempting to get within a one-block range by path-finding around obstacles in their way. When a player is within one block, they will emit a sibilant hiss and ignite a 1.5-second fuse. If the player leaves this one-block range within 1.5 seconds, the Creeper will abort its countdown and resume its attempts to reach the player. But if the player is still within one block of the Creeper when the fuse runs out, the Creeper detonates, destroying blocks in the area as well as significantly damaging the player.
Unlike most mobs, Creepers remain a persistent threat during the day: Aside from the Slime, Creepers are the only hostile Overworld mob that neither burns nor becomes peaceful in the sunlight. (And Creepers are a great deal more threatening than Slimes.)
Creepers have one weakness: Ocelots and their tamed counterparts, cats, frighten Creepers away. In effect, a cat provides a radius of protection into which a Creeper will not enter. This protection can be stationary, or it can be made to follow the player, as tamed cats can be instructed to do either.
Creepers are uniquely devastating in many respects, but it is two simple rules in their path-finding that give Creepers their reputation for subtle intelligence. First, Creepers are always trying to get within one block of the player. Many succeed (silence helps)---but not all by sneaking up from behind. Those that succeed from a player's left, right, or above will inevitably show the traits of a calculated ambush predator---whether lying in wait to pounce from around a corner, to drop down from a ledge above, etc. Second, Creepers will attempt to move around any obstacles between them and the player. Part of this path-finding requires them to move sideways while they are still behind the obstacle. From many angles, and especially if the player is moving, the Creeper can appear to be evading or attempting to hide from the player upon being spotted.
Before 1.2, they would circle to your left. Starting in snapshot 12w05a, they got the same updates that zombies and skeletons got.
A Slime is a green cube shaped hostile mob. There are 3 sizes found naturally in-game: big, small, and tiny. With mods, there can be bigger sizes than these. Unlike other mobs, Slimes don't target players, they just move toward the closest one, even if shot by a skeleton or if the player is through a wall. When no player is within 16 blocks, they hop in one direction and run into walls then turn. Because they don't target a particular player, they won't attack you if you attack them in creative. However, if a big or medium slime touches you, you will take 1 heart (2 hit points) of damage for a medium, and 1 and a half hearts (3 hit points) of damage for a big. Slimes will not avoid fire, deep falls, or other things that hurt them, making them easy to trap and kill. They will also not attempt to kill NPC villagers. As of snapshot 14w06b, Slimes can swim, but before this they would sink to the bottom of a body of water and try to hop out, but to no avail, making it look as though they were struggling to get out. Because they are living mobs, they will eventually drown.
Ghasts can seek out players from 100 blocks away. Once they come within range and can see you, they shoot fireballs, which have 1/3 the explosive force as a Creeper and light surrounding blocks on fire. Unlike other hostile mobs, Ghasts will not attempt to draw close to the player once aggravated, but will instead hover about 24 blocks from the player, firing repeatedly at them. They do not become aggressive under any circumstances in creative mode, but it has been confirmed that this is a bug. This bug happens because ghasts don't have a search mode. They are only found in The Nether or spawned via spawn eggs
 Spider Jockey
The spider controls how both mobs move. The spider acts like a normal spider, and the skeleton acts like a normal skeleton, except its movement is determined by the spider it rides upon. The skeleton's arrows will sometimes damage the spider jockey itself. This can be encouraged by digging a 1 block wide hole 3 blocks straight down and simply standing in it; the spider will sit over top of the hole and the skeleton will fire straight down in an attempt to hit the player, but will only end up hitting its mount. Occasionally, the skeleton will get off the spider. This will also happen if you log out and back in. They are very rare and have a 1% chance to be spawned with a spider spawn egg
Blazes fly if they see you. About every 10 seconds, they will catch fire, then shoot 3 fireballs at you in quick succession. The fireballs will set the ground alight wherever they land. They tend to strafe right (your left if you're facing them) when attacking. Blazes are damaged by water and snowballs, as well as rain/snow.
 Ender Dragon
The Ender Dragon is one of Minecraft's two bosses. Only one spawns in the End at a time, and killing it is one of the two ways to exit the End, other than dying. Killing the Ender Dragon is the only way to finish Minecraft. It can regenerate health by flying near one of the multiple End Crystals in the End. It has 100 hearts, which makes it quite difficult to kill without a diamond sword and bow. The Ender Dragon only takes 1/4 damage from anything that doesn't hit it in the face. The Ender Dragon will fly away from the player if they look at it, except when it charges them. Only rarely will the ender dragon multiply when the game is saved in the middle of the battle, this is a glitch.
The Wither is an undead type of mob that is spawned when the player chooses, like snow golems and iron golems. When spawned by the player, they will be invulnerable for about 10 seconds, then they will create a huge explosion. They fly 4 blocks above the player. Their three heads (projectiles) will attack the player and all mobs that are not undead. Their heads will cause an explosion like a ghast fireball, but instead of fire, it causes the Wither potion effect. Withers will break blocks between it and the player. When the wither reaches half health, it will stop flying, will be immune to arrows and also will start regenerating hp.