Vibration is becoming a more important element in design of telescope structures as these structures become larger and more compliant and include higher bandwidth actuation systems. This paper describes vibration damping methods available for current and future implementation and compares their effectiveness for a model of the Large Synoptic Survey Telescope (LSST), a structure that is actually stiffer than most large telescopes. Although facility and mount design, structural stiffening and occasionally vibration isolation have been adequate in telescopes built to date, vibration damping offers a mass-efficient means of reducing vibration response, whether the vibration results from external wind disturbances, telescope slewing, or other internal disturbances from translating or rotating components. The paper presents several damping techniques including constrained layer viscoelastics, viscous and magnetorheological (MR) fluid devices, passive and active piezoelectric dampers, tuned mass dampers (vibration absorbers) and active resonant dampers. Basic architectures and practical implementation considerations are discussed and expected performance is assessed using a finite element model of the LSST. With a goal of reducing settling time during the telescope's surveys, and considering practicalities of integration with the telescope structure, two damping methods were identified as most appropriate: passive tuned mass dampers and active electromagnetic resonant dampers.