The classics
Wolves tame with bones (roughly a 1-in-3 chance per bone) and fight beside you, targeting whatever you attack. Cats tame with raw cod or salmon, creep away from creepers — making tamed cats the cheapest creeper deterrent in the game. Horses tame by repeated mounting attempts; a saddle (dungeon treasure) makes them rideable and they scale walls of 1.5 blocks, transforming early travel.
The rest of the barn
Parrots tame with seeds (keep them away from cookies — cookies poison parrots), llamas tame by riding until they stop bucking and carry chest caravans, foxes need the sneaking-breeding trick (spawn from two trust-gained foxes), and axolotls tame with a water bucket of tropical fish, fighting fish-hostile mobs in your water battles.
Why tame at all
Wolves and cats are combat/utility, horses and llamas are transport, and tamed animals also serve farms and aesthetics. Feeding tamed animals their food heals them and, for wolves and cats, triggers breeding — two tamed animals of the same type with food make a baby.
