Minecraft wiki entry for The_second_day, associated text: Wheat is the original crop, used to make bread, cake, cookies, and hay bales. Use seeds lure and breed chickens. Wheat itself does the same for cows and sheep. Wheat and hay bales are also used to heal horses and llamas, and to speed up their taming, although they do not attract these animals' attention.
Sugar cane is important because it's needed to make paper, and you may need a lot of that (along with leather, see below) for enchanting. Look for it at the edge of any body of water.
Pumpkins can be scattered in the wild, or can be found in taiga and snowy taiga‌[BE only] villages. They can be used to make pumpkin pies, or be carved using shears into carved pumpkins, which are used to craft jack o'lanterns, worn as a helmet to avoid aggravating endermen, or used to build a snow golem. Pumpkin seeds can also be found in treasure chests, and occasionally offered by wandering traders if you have emeralds.
Carrots, potatoes and beetroots are additional food crops, all of which are grown similarly to wheat (and can share space in your wheat farm). The first two are rarely dropped by slain zombies; only a single item is dropped, but by planting that one, you can multiply it until you have a respectable crop. All three can be found in the farms of a village.
All three of these can be used to lure and breed pigs.
Carrots can also be used to lure and breed rabbits.
Carrots, once combined with gold nuggets into golden carrots, can be used to breed horses (see below).
Cactus is mildly useful for barriers and traps, and is also the only renewable source for green dye. It is found only in deserts, badlands, and in flower pots in igloo basements.
Melons are found in jungles, though later you might be able to find melon seeds in treasure chests, buy them, or find them in savanna villages.
Cocoa beans are another jungle specialty. They're the only source of brown dye, and also allow you make cookies!
Bamboo is the newest addition to the jungle; if you can get hold of some, you can craft the remarkably useful scaffolding blocks, and breed pandas with them.