We study the effects of social influences in opinion dynamics. In particular, we define a simple model, based on the majority rule voting, in order to consider the role of conformity. Conformity is a central issue in social psychology as it represents one of people's behaviors that emerges as a result of their interactions. The proposed model represents agents, arranged in a network and provided with an individual behavior, that change opinion in function of those of their neighbors. In particular, agents can behave as conformists or as nonconformists. In the former case, agents change opinion in accordance with the majority of their social circle (i.e., their neighbors); in the latter case, they do the opposite, i.e., they take the minority opinion. Moreover, we investigate the nonconformity both on a global and on a local perspective, i.e., in relation to the whole population and to the social circle of each nonconformist agent, respectively. We perform a computational study of the proposed model, with the aim to observe if and how the conformity affects the related outcomes. Moreover, we want to investigate whether it is possible to achieve some kind of equilibrium, or of order, during the evolution of the system. Results highlight that the amount of nonconformist agents in the population plays a central role in these dynamics. In particular, conformist agents play the role of stabilizers in fully-connected networks, whereas the opposite happens in complex networks. Furthermore, by analyzing complex topologies of the agent network, we found that in the presence of radical nonconformist agents the topology of the system has a prominent role; otherwise it does not matter since we observed that a conformist behavior is almost always more convenient. Finally, we analyze the results of the model by considering that agents can change also their behavior over time.