We present an investigation of the ultraviolet and X-ray spectra of the Seyfert 1.5 galaxy Markarian 817. The ultraviolet analysis includes two recent observations taken with the Cosmic Origins Spectrograph in August and December 2009, as well as archival spectra from the International Ultraviolet Explorer and the Hubble Space Telescope. Twelve Ly-alpha absorption features are detected in the 1997 GHRS and 2009 COS spectra - of these, four are associated with high-velocity clouds in the interstellar medium, four are at low-significance, and the remaining four are intrinsic features, which vary between the GHRS and COS observations. The strongest intrinsic absorber in the 1997 spectrum has a systemic velocity of ~ -4250 km/s. The corresponding feature in the COS data is five times weaker than the GHRS absorber. The three additional weak (equivalent width from 13-54 mA) intrinsic Ly-alpha absorbers are at systemic velocities of -4100 km/s, -3550 km/s, and -2600 km/s. However, intrinsic absorption troughs from highly ionized C IV and N V, are not detected in the COS observations. No ionized absorption signatures are detected in the ~ 14 ks XMM-Newton EPIC spectra. The factor of five change in the intrinsic Ly$alpha$ absorber is most likely due to bulk motions in the absorber, since there is no drastic change in the UV luminosity of the source from the GHRS to the COS observations. In a study of variability of Mrk 817, we find that the X-ray luminosity varies by a factor of ~40 over 20 years, while the UV continuum/emission lines vary by at most a factor of ~2.3 over 30 years. The variability of the X-ray luminosity is strongly correlated with the X-ray power-law index, but no correlation is found with the simultaneous optical/UV photometry.