Dynamic properties of dilute solutions of neutral and charged dendrimers with explicit excluded-volume, electrostatic, and hydrodynamic interactions have been investigated by Brownian dynamics simulation. Three different types of motions in dendrimers up to g = 5 generations have been considered: the motion of a dendrimer as a whole; the size and shape fluctuations (pulsations); the local reorientations of the individual monomers. The influence of the excluded-volume, electrostatic, and hydrodynamic interactions on these motions has been studied. The characteristic relaxation times have been compared with the theoretical predictions of the Rouse and Zimm models. The self-diffusion of a dendrimer can be described with the help of the preaveraged Zimm approach, and a dendrimer may be considered as an impenetrable sphere with the hydrodynamic radius Rh. For both neutral and charged dendrimers the hydrodynamic radius is smaller than the gyration radius Rg. The dynamics of the size fluctuations for a dendrimer with rigid spacers differs significantly from the theoretical predictions for a dendrimer with flexible spacers. The relaxation of these fluctuations is weakly sensitive to the presence of the hydrodynamic interactions, and the behavior of a dendrimer is close to that of an elastic body in a viscous medium. The local orientational mobility of individual monomers is significantly influenced by the ionization of the terminal groups.