New fully relativistic calculations of radiative rates and electron impact excitation cross sections for Fe XVI are used to determine theoretical emission-line ratios applicable to the 251 - 361 A and 32 - 77 A portions of the extreme-ultraviolet (EUV) and soft X-ray spectral regions, respectively. A comparison of the EUV results with observations from the Solar Extreme-Ultraviolet Research Telescope and Spectrograph (SERTS) reveals excellent agreement between theory and experiment. However, for emission lines in the 32 - 49 A portion of the soft X-ray spectral region, there are large discrepancies between theory and measurement for both a solar flare spectrum obtained with the X-Ray Spectrometer/Spectrograph Telescope (XSST) and observations of Capella from the Low Energy Transmission Grating Spectrometer (LETGS) on the Chandra X-ray Observatory. These are probably due to blending in the solar flare and Capella data from both first order lines and from shorter wavelength transitions detected in second and third order. By contrast, there is very good agreement between our theoretical results and the XSST and LETGS observations in the 50 - 77 A wavelength range, contrary to previous results. In particular, there is no evidence that the Fe XVI emission from the XSST flare arises from plasma at a much higher temperature than that expected for Fe XVI in ionization equilibrium, as suggested by earlier work.