The first observations of ultraviolet spectral line profiles and intensities from the extended solar corona (i.e., more than 1.5 solar radii from Sun-center) were obtained on 13 April 1979 when a rocket-borne ultraviolet coronagraph spectrometer of the Harvard-Smithsonian Center for Astrophysics made direct measurements of proton kinetic temperatures, and obtained upper limits on outflow velocities in a quiet coronal region and a polar coronal hole. Following those observations, ultraviolet coronagraphic spectroscopy has expanded to include observations of over 60 spectral lines in coronal holes, streamers, coronal jets, and solar flare/coronal mass ejection (CME) events. Spectroscopic diagnostic techniques have been developed to determine proton, electron and ion kinetic temperatures and velocity distributions, proton and ion bulk flow speeds and chemical abundances. The observations have been made during three sounding rocket flights, four Shuttle deployed and retrieved Spartan 201 flights, and the Solar and Heliospheric Observatory (SOHO) mission. Ultraviolet spectroscopy of the extended solar corona has led to fundamentally new views of the acceleration regions of the solar wind and CMEs. Observations with the Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO revealed surprisingly large temperatures, outflow speeds, and velocity distribution anisotropies in coronal holes, especially for minor ions. Those measurements have guided theorists to discard some candidate physical processes of solar wind acceleration and to increase and expand investigations of ion cyclotron resonance and related processes. Analyses of UVCS observations of CME plasma properties and the evolution of CMEs have provided the following: temperatures, inflow velocities and derived values of resistivity and reconnection rates in CME current sheets, compression ratios and extremely high ion temperatures behind CME shocks, and three dimensional flow velocities and magnetic field chirality in CMEs. Ultraviolet spectroscopy has been used to determine the thermal energy content of CMEs allowing the total energy budget to be known for the first time. Such spectroscopic observations are capable of providing detailed empirical descriptions of solar energetic particle (SEP) source regions that allow theoretical models of SEP acceleration to be tailored to specific events, thereby enabling in situ measurements of freshly emitted SEPs to be used for testing and guiding the evolution of SEP acceleration theory. Here we review the history of ultraviolet coronagraph spectroscopy, summarize the physics of spectral line formation in the extended corona, describe the spectroscopic diagnostic techniques, review the advances in our understanding of solar wind source regions and flare/CME events provided by ultraviolet spectroscopy and discuss the scientific potential of next generation ultraviolet coronagraph spectrometers.