We investigate the role of conflicts in pedestrian traffic, i.e., situations where two or more people try to enter the same space. Therefore a recently introduced cellular automaton model for pedestrian dynamics is extended by a friction parameter mu. This parameter controls the probability that the movement of all particles involved in a conflict is denied at one time step. It is shown that these conflicts are not an undesirable artifact of the parallel update scheme, but are important for a correct description of the dynamics. The friction parameter mu can be interpreted as a kind of an internal local pressure between the pedestrians which becomes important in regions of high density, occurring, e.g., in panic situations. We present simulations of the evacuation of a large room with one door. It is found that friction has not only quantitative effects, but can also lead to qualitative changes, e.g., of the dependence of the evacuation time on the system parameters. We also observe similarities to the flow of granular materials, e.g., arching effects.