The production of molecular hydrogen in the radiolysis of isotactic polypropylene (PP), poly(methyl methacrylate) (PMMA), and polystyrene (PS) with protons and carbon ions has been investigated. Previous experimental data on the above polymers with gamma -ray and helium ion irradiations have been combined with similar studies on high-density polyethylene (PE) to give a comprehensive survey of the dependence of molecular hydrogen yields on particle linear energy transfer, LET, in the range 0.2-800 eV/nm. The radiation chemical yields of molecular hydrogen are very dependent on LET and generally increase with increasing LET. However, the relative change in hydrogen yield as a function of LET is very different for the various polymers. It appears that with increasing high LET the hydrogen yields for each of the polymers are approaching the same value. This observation suggests that the radiolytic source of molecular hydrogen is similar for all of the polymers and increases with increasing LET of the irradiation. Unexpectedly high yields of molecular hydrogen can have implications in many fields including those that involve heavy charged particles and intense photon sources.