NASAs Great Observatories have opened up the electromagnetic spectrum from space, providing sustained access to wavelengths not accessible from the ground. Together, Hubble, Compton, Chandra, and Spitzer have provided the scientific community with an agile and powerful suite of telescopes with which to attack broad scientific questions, and react to a rapidly changing scientific landscape. As the existing Great Observatories age, or are decommissioned, community access to these wavelengths will diminish, with an accompanying loss of scientific capability. This report, commissioned by the NASA Cosmic Origins, Physics of the Cosmos and Exoplanet Exploration Program Analysis Groups (PAGs), analyzes the importance of multi-wavelength observations from space during the epoch of the Great Observatories, providing examples that span a broad range of astrophysical investigations.