High-level ab initio molecular orbital calculations have been carried out to describe the potential energy surfaces for a series of systems corresponding formally to dimer ions of molecular hydrogen with an inert-gas atom or a first- or second-row hydride [X...H-2]+, where X=He, Ne, Ar, Kr, HF, HCl, H2O, H2S, NH3, and PH3. Of the [XH2]+ ion complexes, [Ne...H-2]+, [Ar...H-2]+, [Kr...H-2]+, and [HFH...H]+ lie in wells of significant depth and should be experimentally observable. The energetics of ion-molecule reactions associated with the [XH2]+ systems have been examined in detail. The reactions include proton- and hydrogen-transfer reactions and hydrogen-exchange reactions. Pathways and transition structures for scrambling of hydrogen atoms within the [XH2]+ complexes, some of which are relevant to the exchange reactions, have also been determined.