An outline of numerical path integral techniques which allows one to treat the rotational component of molecular motion is given in a unified framework. Special attention is paid to the particular aspects of this treatment depending on the dimension of the subspace for rotations, which leads to optimized methods for one-, two- and three-dimensional rigid rotors. The implications of the coupling between rotational and nuclear spin degrees of freedom, due to the symmetry requirement of the total wave function under exchange of identical particles, are discussed. Several recent applications of path integral simulations of rigid rotors are presented. These examples include both strongly simplified and very realistic models for investigating the properties of molecular impurities and clusters, rotors physisorbed on surfaces, and condensed molecular phases. Where available, the results of approximate calculations based on quasi-classical, quasi-harmonic and mean-field theories are compared to the path integral simulations.