The first cultural influence you'll probably think of when you see the tauren and walk around in their villages is "Native American." That's fine as far as it goes, but you should remember that they're mainly based on the stereotypical image of what Native Americans are rather than their actual reality. I'm hardly an expert on Native Americans, however, so rather than try and speak for these differences, I'm just going to put the whole issue aside and take tauren as tauren rather than parallels to any human culture. Besides, aside from certain aspects of architecture, music, clothing, and mythology, the tauren are really their own species. They are quite general enough to remind us of all kinds of different cultures around the world, many of whom cherish the earth, revere their ancestors, and try to live in harmony with the world.
Some people say that the tauren are the noblest and most peaceful of the races in World of Warcraft, but for most of their history, they have been at war with the vicious centaur -- though not by choice. The centaur have always been very hostile towards tauren, driving them out of their ancestral homelands, slaughtering them and even cannibalizing them whenever possible. In a way, the centaur seem like four-legged versions of the nastier trolls who never joined the Horde. When Thrall came to Kalimdor and encountered the tauren in the midst of their struggle against the centaur, it marked the beginning of one of the greatest changes in tauren history.
In the Beginning...
Tauren mythology contains some of the most interesting background lore in the entire Warcraft series, and evokes some powerful imagery. They say that, "before the Age of Memory," the Earthmother created the world by breathing upon "the golden mists of dawn," and transforming them into "endless fields of flowing wheat and barley." As she gazed lovingly upon her newly formed land, she opened her right eye to spread give it warmth and light, then opened her left eye, which "gave peace and sleep to the stirring creatures of the dawning." Wherever the arms of the Earthmother caressed their shadows over the land, there a people rose up out of the rich soil -- the tauren, who know themselves in their own language as the Shu'halo.
It is said that some of the ancient tauren lost their way as they "listened to dark whispers from deep beneath the world" (probably the "Old Gods"), and caused the Earthmother to tear out her eyes in grief, and "set them spinning across the endless starry skies" as the sun and the moon. But the Earthmother never abandoned her children. She taught them to hunt, and guided them while they learned the ancient ways of the druid (and, although druidic magic was gradually lost to the tauren of the past, they have begun relearning it in recent years). The Earthmother guided the tauren even while they suffered under the cruel oppression of the centaur and were driven from their native homeland, forced to "roam the endless plains as nomads forever after" until "one day hope would return -- and the scattered tribes of the Shu'halo would find a new home under the loving arms of the Earthmother."
And so it came to pass...
Growing up as a tauren, your character would have lived most of his or her childhood in the Barrens, scraping by on the meager living that could be made there. At that time the tauren tribes moved their tent cities all over the region as the seasons and weather changed, just trying to survive the harshness of the landscape and the centaur raids. All the tribes were suffering greatly; life was hard, and it seemed the centaur could wipe them out at any moment.
The arrival of the orcs and trolls of the Horde in Kalimdor changed everything for the tauren. Even from their first meetings, all three races could see that they shared common goals. The tauren had the deeply spiritual shamanistic culture that the orcs were trying to restore in the Horde, and the orcs had the power and will to assist the tauren in driving back their enemy and retaking their ancestral homelands.
Cairne Bloodhoof, chief of the Bloodhoof tribe, was the first to make contact with Thrall and the Horde, and also the primary commander of the tauren in the deciding battles against the centaur. Having retaken Mulgore and established a permanent home for his people after so many centuries wandering around in the Barrens, he welcomed all tauren tribes in the new mesa-city of Thunder Bluff, and naturally came to be leader of his entire race, as all the tribes gradually united under him and the new Horde.
But not all the tauren are happy with Cairne's leadership. The Grimtotem tribe, in particular, view all other races as enemies, and seek to overthrow Cairne's rule of the tauren. In many ways, they are tauren equivalent of a mafia: their Elder Crone Magatha Grimtotem maintains the facade of allegiance to Cairne and the Horde within the city of Thunder Bluff, but commands her tribesmen in other settlements to anyone who comes near. They sometimes attack even tauren who are known to associate themselves with other races. Oddly, the only race they do not seem to hate is the Forsaken, a few of which have even become part of the Grimtotem clan. It is because of this association that the forsaken were allowed a cave within Thunder Bluff to use for their own mysterious purposes, although no one knows what sort of betrayal the Forsaken and the Grimtotem have planned for their hosts. Most other tauren quite rightly treat both groups with deep suspicion.
Excepting the Grimtotems, of course, tauren generally view all other races amiably, and give them the benefit of the doubt. They are especially close to the orcs of course, due to their common vision of the world and mutual assistance in times of need. Some tauren even look past their mistrust of the Forsaken and hope to help them cure themselves of their undead condition. The blood elves, on the other hand, reek of arcane magic, and the tauren have a great deal of difficulty around this poisonous energy. Ironically, they generally have no enmity against the Alliance unless physically threatened, and even have a deep respect for the night elves, whom they associate with their ancient myths of the children of the moon -- the luminous left eye of the Earthmother herself.
...here you stand.
Your tauren character would have gained maturity around the age of 50, much like a gnome or a dwarf. Most tauren are considered middle-aged at about 75, elderly at 95, and venerably old at 110, though rare heroes have been known to live as long as 150. From the beginning, your character would have been taught the love of the hunt, and the balance and reciprocity all people must share with nature. Whatever you take from the world, you would strive to give back in whatever way you can.
This dual training makes the tauren at once serene and cultured, yet fearsomely implacable when drawn into conflict. The tauren themselves don't feel so enormous when amongst themselves, but when they encounter other races, they can't help but notice how thin and small they seem. Tauren even get stuck from time to time while trying to get around in the cramped areas that other races live in. Their hooves might also cause slight issues on hard or slippery surfaces other races seem to prefer to the tender soil of the earth itself. Yet on the battlefield, tauren stomp their hooves against the earth with such force that the smaller creatures are stunned for a moment while they regain their balance.
For further reading about the tauren, check out WoWWiki's encyclopedic information, as well as Dramatis-Personae's tauren quick-start page. Also, take a good look at tauren mythology, as this aspect of their history matters more to tauren than it does to other races.