We analyze ultraviolet (~1500 A) images of the old open clusters M67, NGC 188, and NGC 6791 obtained with Ultraviolet Imaging Telescope (UIT) during the second flight of the Astro observatory in March 1995. Twenty stars are detected on the UIT image of M67, including 11 blue stragglers, seven white dwarf candidates, and the yellow giant -- white dwarf binary S1040. The ultraviolet photometry of the blue stragglers F90 (S975) and F131 (S1082) suggests that these stars have hot subluminous companions. We present a semi-empirical integrated ultraviolet spectrum of M67, and show that the blue stragglers dominate the integrated spectrum at wavelengths shorter than 2600 A. The number of white dwarfs in M67 is roughly consistent with the number expected from white dwarf cooling models. Eight candidate sdB/sdO stars are detected in NGC 6791, and two are detected in NGC 188. The luminosity range 1.10 < log L/Lsun < 1.27, derived from the ultraviolet photometry of the six sdB candidates, is consistent with theoretical models of metal-rich hot horizontal branch (HB) stars. The fraction of hot HB stars in both NGC 6791 and NGC 188 is about 30%, implying that the integrated spectra of both clusters should show a UV turnup at least as strong as that observed in any elliptical galaxy.