Generally speaking, the animals that are easiest to domesticate are dogs, cats, pigs, sheep, horses, chickens, cows and goats. These animals have mental and social traits that make them easier to tame and less dangerous than alternatives.
Some examples of animals that can be domesticated and tamed from young ages include ducks, guinea pigs, camels, ferrets and some species of birds, such as pigeons. These animals all conform to a certain criteria that make them easier to tame, including a strong social order, a diverse appetite, a quick lifespan, and comfort with breeding in close-quarters. Animals that strongly oppose traits such as these are very poor choices for domestication.
Animals considered too wild to tame or too difficult to do so tend to be bigger than humans or have specific traits in their biology or behavior that makes taming them unfeasible. Antelopes, for example, require a large area in order to breed. Rhinos and hippos cannot be domesticated because of their size and extreme aggression when threatened. Animals that cannot recognize humans as the leader or master of the pack, such as big cats, are unlikely to be tamed at all, because the animal is not likely to modify its behavior.