Aims. The Landé g-factor is an important parameter in astrophysical spectropolarimetry, used to characterize the response of a line to a given value of the magnetic field. The purpose of this paper is to present accurate Landé g-factors for states in B II, C I-IV, Al I-II, Si I-IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II. Methods. The multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2K, are employed in the present work to compute the Landé g-factors for states in B II, C I-IV, Al I-II, Si I-IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II. The accuracy of the wave functions for the states, and thus the accuracy of the resulting Landé g-factors, is evaluated by comparing the computed excitation energies and energy separations with the National Institute of Standards and Technology (NIST) recommended data. Results. All excitation energies are in very good agreement with the NIST values except for Ti II, which has an average difference of 1.06%. The average uncertainty of the energy separations is well below 1% except for the even states of Al I; odd states of Si I, Ca I, Ti II, Zr III; and even states of Sn II for which the relative differences range between 1% and 2%. Comparisons of the computed Landé g-factors are made with available NIST data and experimental values. Analysing the LS-composition of the wave functions, we quantify the departures from LS-coupling and summarize the states for which there is a difference of more than 10% between the computed Landé g-factor and the Landé g-factor in pure LS-coupling. Finally, we compare the computed Landé g-factors with values from the Kurucz database.