Minecraft wiki entry for Farming, associated text: Wheat, Carrot, Potato, Beetroot farming, and Sweet Berries
Farming wheat, carrots, potatoes, beetroots, and Sweet Berries
Pumpkin and Melon farming
Farming pumpkins and melons
Vine farming
Vines can be farmed for use instead of ladders, decoration, or crafting mossy stone bricks or mossy cobblestone. The Nether also offers weeping vines and twisting vines. In all cases they are initially planted on a block (green vines on the side of the block, weeping vines on the bottom, twisting vines on the top), after which they can be allowed to grow naturally or force-grown with bonemeal. All are harvested with shears, though the Nether vines can be harvested at a 1/3 drop rate without tools.
Kelp farming
Farming kelp for fuel or decoration.
Bamboo farming
Farming bamboo for fuel, sticks or scaffolds.
Sugar Cane farming
Farming sugar canes to make paper and sugar.
Chorus Fruit farming
Farming chorus fruit for food and popped chorus fruit, which makes purpur blocks and end rods.
Mushroom farming
Farming mushrooms for use in mushroom stew or creating huge mushrooms. They can be farmed in darkness, in the Nether, or (in any light) on mycelium or podzol blocks.
Nether Wart farming
Farming nether wart for use in brewing.