Recently we have demonstrated that the applicability of the Tkatchenko-Scheffler (TS) method for calculating dispersion corrections to density-functional theory can be extended to ionic systems if the Hirshfeld method for estimating effective volumes and charges of atoms in molecules or solids (AIM's) is replaced by its iterative variant [T. Bucko, S. Lebegue, J. Hafner, and J. Angyan, J. Chem. Theory Comput. 9, 4293 (2013)]. The standard Hirshfeld method uses neutral atoms as a reference, whereas in the iterative Hirshfeld (HI) scheme the fractionally charged atomic reference states are determined self-consistently. We show that the HI method predicts more realistic AIM charges and that the TS/HI approach leads to polarizabilities and C-6 dispersion coefficients in ionic or partially ionic systems which are, as expected, larger for anions than for cations (in contrast to the conventional TS method). For crystalline materials, the new algorithm predicts polarizabilities per unit cell in better agreement with the values derived from the Clausius-Mosotti equation. The applicability of the TS/HI method has been tested for a wide variety of molecular and solid-state systems. It is demonstrated that for systems dominated by covalent interactions and/or dispersion forces the TS/HI method leads to the same results as the conventional TS approach. The difference between the TS/HI and TS approaches increases with increasing ionicity. A detailed comparison is presented for isoelectronic series of octet compounds, layered crystals, complex intermetallic compounds, and hydrides, and for crystals built of molecules or containing molecular anions. It is demonstrated that only the TS/HI method leads to accurate results for systems where both electrostatic and dispersion interactions are important, as illustrated for Li-intercalated graphite and for molecular adsorption on the surfaces in ionic solids and in the cavities of zeolites.