In this work, nine new synthetic alkali- and rare-earth metal crichtonite-type compounds with AB3C18O38 general formula are presented. The effect on the magnetic properties as consequence of the substitution of divalent and trivalent cations in the A site, as well as the introduction of iron at the B and C sites is studied. Ferrimagnetic behavior was identified in the crichtonites CaMn3Ti18O38, BaMn3Ti18O38 and CaFe3Ti18O38, which changes to a spin-glass type for the BaMn3Ti14Fe4O38 and A-trivalent REMn3Ti18O38 (RE = La, Ce and Nd), LaFe3Ti18O38 and LaMn3Ti13Fe5O38. A comprehensive comparison of the AC and DC magnetic measurements for whole series along with the FiM structure obtained by neutron powder diffraction is discussed. These results will expand the comprehension on this almost unexplored magnetic family of compounds.