From Minecraft Wiki
Farming refers to the systematic production of Renewable resource. It is usually used to get Blocks, Food, Experience and more things. Specific types of farming include:
 Mob Farming
- Animal farming
- Using wheat, seeds, and carrots to breed animals, to be slaughtered for their products or used in Egg, Milk, or Wool Farming.
- Mob Farming
- Creating spawn rooms for hostile mobs, to be killed for their drops.
- Villager Farming
- Farming Villagers by creating houses, doors, or curing spawned Villager Zombies.
 Experience Farming
- Spawner Farming
- Waiting at an active monster spawner for monsters to spawn. This includes mobs that do not spawn naturally without the use of spawners, notably Cave Spiders.
 Food Farming
- Wheat, Carrot and Potato Farming
- Farming wheat, carrots, and potatoes, the three staple food crops. (Combined version of their original pages.)
 Block Farming
- Cactus Farming
- Farming cacti for cactus green dye or traps.
- Cobblestone Farming
- Creating a stone or cobblestone generator for self-repairing shelters or harvesting.
- Obsidian Farming
- Creating an Obsidian generator for Obsidian intensive builds.
- Ice Farming
- Farming ice using a self-refilling rink.
- Pumpkin Farming
- Farming pumpkins for use in pumpkin pie, Jack 'o' Lanterns or Golems.
- Vine Farming
- Farming vines for use instead of ladders or for decoration.
- Tree Farming
- Farming Trees for wood, saplings, apples, or charcoal.
 Item Farming
- Iron Farming
- Farming iron ingots by killing the Iron Golems spawned in large Villages.
- Gold Farming
- Farming gold nuggets by killing the Zombie Pigmen which spawn in The Nether or near Nether Portals in The Overworld.
- Chicken Egg Farming
- Farming eggs for use in cake, pumpkin pie or creating chickens.
- Cocoa Bean Farming
- Farming cocoa beans for use in cookies or creating brown wool.
- Mushroom Farming
- Farming mushrooms for use in mushroom stew or creating huge mushrooms.
- Nether Wart Farming
- Farming Nether Wart for use in Brewing.
- Snow Farming
- Trapping a Snow Golem and digging the snow it produces.
- Sugar Cane Farming
- Farming sugar cane for books and sugar, which is required for cake and pumpkin pie.