Clusters of polycyclic aromatic hydrocarbon (PAH) molecules are modeled using explicit all-atom potentials using a rigid-body approximation. The considered range of PAHs goes from pyrene (C10H8) to circumcoronene (C54H18) and clusters containing between 2 and 32 molecules are investigated. In addition to the usual repulsion-dispersion interactions, electrostatic point-charge interactions are incorporated, as obtained from density functional theory calculations. The general electrostatic distribution in neutral or singly charged PAHs is reproduced well using a fluctuating-charges analysis, which provides an adequate description of the multipolar distribution. Global optimization is performed using a variety of methods, including basin-hopping and parallel tempering Monte Carlo. We find evidence that stacking the PAH molecules generally yields the most stable motif. A structural transition between one-dimensional stacks and three-dimensional shapes built from multiple stacks is observed at larger sizes, and the threshold for this transition increases with the size of the monomer. Larger aggregates seem to evolve toward the packing observed for benzene in bulk. Difficulties met in optimizing these clusters are analyzed in terms of the strong anisotropy of the molecules. We also discuss segregation in heterogeneous clusters and vibrational properties in the context of astrophysical observations.