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Interest in astrophysical sources of charge exchange X-rays has been growing steadily since the discovery of X-ray emission from the comet Hyakutake with ROSAT in 1996. Since then, charge exchange has been observed between solar wind ions and neutrals in the geocorona and in the atmospheres of Mars and Jupiter. Charge exchange with interstellar neutrals within the heliosphere between solar wind ions and neutral hydrogen and helium from the interstellar medium is now acknowledged as contributing a considerable (although currently unknown) fraction of the soft X-ray background. We make a brief survey of the heliospheric, Galactic, and extragalactic systems in which charge exchange has been observed or is predicted to take place. Experiments measuring velocity dependent cross-section and line ratios for Lyman-series lines and He-like triplets are needed to check current theoretical models of charge exchange emission and aid interpretation of observations. We point out a number of systems that are of astrophysical interest that could be the subject of future laboratory investigations, particularly velocity dependent line ratios of the X-ray emission produced by charge exchange between highly ionized common elements (such as O, C, Ne, and Fe) and atomic hydrogen and helium. To begin to address the need for laboratory data we have measured velocity dependent Ly-series line ratios for C6+ ions interacting with H2, He, and Kr gas targets at Oak Ridge National Laboratory's Ion-Atom Merged-Beams Apparatus. [ABSTRACT FROM AUTHOR]