The equilibrium geometries, energetics, and hyperfine coupling constants for a number of charged magnesium clusters and magnesium-rare gas complexes are investigated using gradient corrected density functional theory. In the study of matrix effects, Mg+ and Mg-2(+) are embedded in matrices with up to 10 neon or argon atoms. For the magnesium ion, we calculate a shift in the isotropic hyperfine coupling constant of 10 G when changing the matrix from Ne to Ar (expt. value : 10.9 G), and for Mg-2(+) the calculated shift is -0.5 G (expt. value = 1.1 G). In the second part of the paper, several different positively charged magnesium clusters with up to six magnesium atoms are optimized, and the resulting geometries, relative energies, and hyperfine coupling constants are compared with experimental data and with previous theoretical studies. Based on the computed averaged hyperfne coupling constants, a reassignment is proposed of the experimentally observed average values (in gauss), -222.5 (Mg+), -105.4 (Mg-2(+)), -69.5 (linear Mg-3(+)), -55.0 (triangular Mg-3(+)), -48.5 (Mg-4(+)), and -34.6 (Mg-5(+)). The corresponding calculated values are -211.6, -100.0, -65.2, -58.7, -48.3, and -33.3 G, respectively. For the hexamer ion, we predict an average hfcc of -28.5 G.