When compared to other laser types, the Free Electron Laser (FEL) provides optimal beam quality for successful atmospheric propagation. Assuming the development and deployment of a mega-watt (MW) class, ground or sea based FEL, this thesis investigates several proposed space applications including power beaming to satellites, the removal of orbital debris, laser illumination of objects within the solar system for scientific study, and interstellar laser illumination for communications. Power beaming simulations are conducted within the Satellite Tool Kit (STK) program to determine the frequency of accesses between a satellite and one or more ground stations for multiple orbital profiles. FEL illumination of orbital debris is modeled to determine the thermal effects on a representative aluminum debris particle. FEL illumination of the Lunar and Martian surfaces is modeled to determine the relative laser and solar spectral intensities at these ranges. FEL illumination at interstellar ranges is modeled and discussed to determine our ability to communicate or detect laser communications over interstellar ranges.