Natural acceleration of charged particles occurs within a variety of physical contexts and through a range of physical processes.``Cosmic'' charged particle acceleration can involve particle energies and energy changes from less than one electron Volt (eV), and on through kilovolt (keV) energies, up to 1018 and perhaps 1020 eV. These acceleration processes can be in the forms of various types of electric fields directed parallel to the magnetic field lines, which are believed chiefly responsible for the energization of the auroral electrons which bombard the Earth's upper atmospheres at high magnetic latitudes to create auroras. There are also ``collisionless'' shock layers in our interplanetary space and well beyond, to energize charged particles in solar and stellar winds. And there may be exotic-and somewhat speculative-processes such as the effect of intense radiation beams associated with non-thermal compact objects, or unipolar electric fields of huge magnitudes near a rotating and accreting black hole. These processes may accelerate particles to even 1020 eV energies. The propagation of such ultra-high energy particles in time and space may be severely modified by quantum gravity effects, which are no longer negligible in these extreme situations.