There are 3 categories of mobs. Passive, which will not attack you under any circumstances, neutral which won't attack unless provoked, and hostile which will attack on sight.
Passive: Passive mobs are as follows: Cows, Chickens, Sheep, Pigs, Ocelots, Horses, Bats, Squids, Villagers, and Mooshrooms. Most passive mobs can be bred and used as a farmable source of food, while some have unique abilities to help the player, such as chickens laying eggs, or villagers trading.
Neutral: The neutral mobs are as follows: Wolves, Zombie Pigmen, Endermen, and the Iron and Snow golems. The wolves won't attack their owner if tamed, but will attack any mob other than creepers that their owner hits. Even players. If untamed, they'll hunt passive mobs like cows and sheep, but will attack the player as a group of however many wolves within the chunk if the player damages even one of them. The Zombie Pigmen are the same mechanic, but don't hunt and are not tamable. The endermen will attack only if either attacked, or if the player looks at them. However, the player can do 3 things to look at an enderman. 1: Use peripherals. 2: Look at it's feet since this doesn't agitate them. 3. Wear a Pumpkin. yeah. A pumpkin. For some strange reason, an enderman doesn't recognize a player when wearing a pumpkin, however will still fight if attacked. It also cannot be tamed nor hunts. The Iron golems can naturally spawn into a large enough village, but if created by a player, will kill hostile mobs but will also attack the player if provoked. Same goes for snow, but it can not naturally spawn.
Hostile: The hostile mobs are as follows: Zombies, Zombie Villagers, Skeletons, Wither Skeletons, Skeleton Jockeys, Creepers, Spiders, Cave Spiders, Silverfish, Blazes, Ghasts, Magma Cubes, Slimes, Witches, and the bosses of minecraft: The Ender Dragon and The Wither. All of them have their respective attacks which are too numerous to list, but are all very dangerous in groups of the same or mixed groups of their mobs. As for the bosses, the Ender Dragon used to be fightable once, and fighting it and succeeding would complete the game. As of 1.9, you can resummon the Ender Dragon to farm it for levels and probably Dragon Eggs, which are the item that spawns on top of the portal that it creates upon death. The Wither, however, will never spawn naturally and must be summoned like a golem. The Wither can be fought and farmed for items called "Nether Stars"which are justly named since it's golemic parts are from the nether. These nether stars can be crafted into items called "Beacons" which can give buffs if put on a 3x3, 3x3/5x5, 3x3/5x5/7x7, or 3x3/5x5/7x7/9x9 platforms of Iron, Gold, Diamond, or Gold blocks to give the player buffs as long as they're in range.