Recent evolutionary theories based on Genetic-Cultural Coevolution say that humans naturally act very much the way we observe them acting today. See Nature Versus Nurture for a summary of why we believe these features are inherent in the human condition. See also Good Or Evil?.
We cooperate with each other a great deal, but we also compete for status and resources. Though the tension between getting along and getting ahead is not something that we talk about a lot, or even think about, in the human condition this conflict is inescapable. Evolutionary Psychology has much to say about the clever (and often unconscious) ways that we negotiate this issue. Evolution has decided for us that believing what you say is more important than knowing what you think (see The Happiness Hypothesis and this paper).
People have innate emotions and motivations that guide them in navigating the world. Though the physical world takes its toll of premature death, the human world is primarily a social construct where success is determined in social interactions, so there is considerably cultural variation in the exact triggers for emotions or way in which motivations play out.
People have a moral sense, or as the Genesis story explains, knowledge of the difference between good and evil. This is an intuitive sense of proper social behavior which primarily concerns itself with maintaining productive cooperation within the group, minimizing conflict between individuals and conflict between individual interests and the group interest. See The Righteous Mind. Although our moral sense is innate, there is a great deal of cultural variation in exactly what is considered moral.
People exist in a context of cultural rules for appropriate behavior (such as laws), and this system is contrived to approximately mesh with the innate framework of moral emotions. Almost everyone mostly follows the rules, but (when nobody is looking) most people succeed in coming up with justifications for why it is o.k. to bend the rules a bit.
Some people (mostly men) live as criminals or bandits on the margins of a society or between settlements. These people gain at least part of their living by taking from others, usually involving at least threats of violence.
Group membership is tremendously important to humans because it is a matter of life or death. We participate in various different social groups, and learn to act appropriately in those contexts, displaying badges of membership, enforcing norms, and showing solidarity against outsiders. In-group/out-group dynamics are prominent.
Groups also compete with each other. If the groups are within a single polity (tribe, country) this competition is usually non-violent, but the rewards in terms of status, political power, access to resources, and winning converts (Mind Share) are very real. Groups may cooperate, but when there is official cooperation (not just overlapping memberships) this often involves competition with other coalitions.
Conflict between polities can turn into warfare. Almost all cultures have established practices where men form groups to fight on behalf of the polity.
We have inherited from our social primate ancestors an attunement to dominance or status rankings, but because we participate in multiple groups and can achieve in many different ways, these rankings are multidimensional and context dependent. We have an innate drive for Social comparison, and this is one of the ways that we have become genetically adapted to participate in Cultural Evolution. We also naturally coordinate group actions through the dynamic of leadership/followership (see Evolutionary Leadership Theory). There is considerable cultural variation in how prestige and power are assigned, the degree of inequality, and fixedness or fluidity of one's status. See Prestige Bias.
We also have strong interest in sexual relationships and high motivation to find desirable sexual partners. One of evolutionary psychology's greatest successes is in explaining how the differences in characteristic male and female sexual behavior arise out of the peculiarities of human reproductive strategies. Modest but statistically solid differences have been found between men and women in areas such as sensory perception. These differences arose because specialization of men and women in different roles allowed evolution to separately optimize the design tradeoffs for each sex. Although there is considerable overlap between male and female abilities and motivations, Genetic-Cultural Coevolution resulted in social construction of gender roles which reinforce this behavioral specialization.