We use conventional and multispeckle dynamic light scattering to investigate the dynamics of a wide variety of jammed soft materials, including colloidal gels, concentrated emulsions, and concentrated surfactant phases. For all systems, the dynamic structure factor f(q,t) exhibits a two-step decay. The initial decay is due to the thermally activated diffusive motion of the scatterers, as indicated by the q(-2) dependence of the characteristic relaxation time, where q is the scattering vector. However, due to the constrained motion of the scatterers in jammed systems. the dynamics are arrested and the initial decay terminates in a plateau. Surprisingly, we find that a final, ultraslow decay leads to the complete relaxation of f(q,t), indicative of rearrangements on length scales as large as several microns or tens of microns. Remarkably, for all systems the same very peculiar form is found for the final relaxation of the dynamic structure factor: f(q,t) approximately exp[-(t/tau s)p], with p approximately equal to 1.5 and tau s approximately q(-1), thus suggesting the generality of this behavior. Additionally, for all samples the final relaxation slows down with age. although the aging behavior is found to be sample dependent. We propose that the unusual ultraslow dynamics are due to the relaxation of internal stresses, built into the sample at the jamming transition, and present simple scaling arguments that support this hypothesis.