Crazy Horse, of the Lakota of North America, had a vision. This vision gave him an owl spirit animal, who would protect him, and the pattern of his face paint. He would be protected in battle. With this power, he would lead his people.
This phenomena is an example of a historical way that warriors gain special abilities in order to fight in battles. The story of Crazy Horse seems remarkable to us, but in no way was it remarkable for the hunting and gathering warrior. In that effort to gain power, the earliest way for the ordinary man to gain power was by gaining an animal spirit to help him. This belief is called totemism. By itself, totemism is not a religion. It is, instead, one aspect of a magico-religious tradition. These totems were generally reserved for the most respected and highest ranking members of the tribe.
Totemism defies the description of both magic and religion because the warrior’s belief only states the obvious: the world is full of spirits. Your communal and personal relationship with those spirits determines the fate of your tribe. If relations are good, then hunting and gathering are good as well. If the relationship sours, then the broken relationship needs mending. To a totemist, this is no more magical or divine than getting along with your family, your clan, or your tribe.
Just as you can make friends and help each other, so too do you build special relationships with the spirits. They can aid and help you just as a friend would, or as an ally. As these spirits possess a magic that you do not, their aid makes you more powerful. Their aid enables you to overcome normal human limitations.
In extreme cases, the person becomes the animal. The form of the animal spirit and the man become interchangeable. Thus, legends of the shape changer originates from this bond.
In D&D, totemism clearly falls to the barbarian and the druid, but not in any coherent matter. The label of “totem” is slapped on some barbarian abilities, but the implication of having an animal spirit on your side is not explored. You get a few special abilities based on those totems, but the totem does not really define your character, which is substantially different from the historical model. There, the totem was everything, defining you.
The druids gains animal companion and wildshape, yet these quite fail at communicating the relationship at the base of the powers. The druid has the hallmarks of totemism, but lacks the actual spirits dominating the belief.
In my opinion, totemism is an area in D&D where almost no one has adequately developed the ideas presented. You see glimpses of the ideas in some classes, but no class comes close to the ideal of Crazy Horse.
A second way of gaining an animal’s power is to eat that animal, especially its heart or its testicles. This is an idea especially entrenched in Africa. We still see it today with aphrodisiacs, which are animal parts said to amplify sexual prowess. The animal contains a vital essence, and you gain it when you consume that animal. (There’s an actual terms for this, but for the life of me, I can’t find it.)
Naturally, the stronger the animal that you kill, the stronger the power that you gain.
Due to this idea’s nature, you just don’t see this type of magic in D&D. Very few independent books even touched on this idea. This type of magic does not nest well with any type of discrete magic system and the subject matter seems rather extreme.
In any event, the fighter does not inherit such a magic system, but for once, nobody else does either.