Mobilities in helium gas for isomers belonging to the major structural families of carbon clusters identified in drift tube studies (chains, monocyclic and bicyclic rings, graphite sheets, and fullerenes and their dimers) have been evaluated by trajectory calculations employing a realistic ion-He interaction potential. For all the species considered, the agreement between the measured and calculated mobilities at room temperature improves by at least a factor of 3 over that obtained with the widely used hard-sphere projection approximation. Furthermore, for 3. large representative sample of clusters belonging to all the above families, the results of trajectory calculations as a function of temperature over the range of 78-360 K are in a good agreement with the measured mobilities. This shows that the C-He pairwise potential is only weakly dependent on the structure and chemical bonding of a carbon cluster. Thus this study demonstrates the universal suitability of trajectory calculations for the accurate prediction of the gas phase mobilities for polyatomic ions with various shapes and sizes, and the uniform superiority of this method over the previously used approximations. In particular, the trajectory calculations for large (n = 120-140) fullerenes show that these cages have near-spherical shapes found by theory, while the projection approximation would erroneously assign them as "buckytubes." It also appears that the mobility may be substantially affected by the degree of char localization on a specific atom in the cluster, especially at low temperatures.