Aims: We develop an accurate and general semi-classical formalism that deals with the definition and the calculation of the collisional depolarizing constants of the levels of simple and complex singly-ionized atoms in arbitrary s-states perturbed by collisions with hydrogen atoms. The case of ions with hyperfine structure is investigated fully. Methods: We obtain potential energy curves based on the MSMA exchange perturbation theory by employing the Unsöld approximation. These potentials enter the Schrödinger equation to determine the collisional T-matrix elements in a semi-classical description. We use the T-matrix elements for the calculation of the collisional depolarization rates of simple atoms. Then, we use these rates to calculate the collisional coefficients in cases of ions with hyperfine structure. Results: We evaluate the collisional depolarization and polarization transfer rates of the ground levels of the ionized alkaline earth metals Be II, Mg II, Ca II, Sr II, and Ba II. We study the variation of the collisional rates with effective principal quantum number n* characterizing an arbitrary s-state of a perturbed simple ion. We find that the collisional rates for simple ions obey simple power laws as a function of n^*. We present direct and indirect formulations of the problem of the calculation of the depolarization and polarization transfer rates of levels of complex atoms and hyperfine levels from those for simple atoms. In particular, the indirect method allows a quick and simple calculation with its simple power-law relations. For the state 4s ^2S{1/2} of Ca II, our computed rate of the destruction of orientation differs from existing quantum chemistry calculations by only 4% at T=5000 K.