The Faint Object Spectrograph (FOS) aboard Hubble Space Telescope has been used in the UV to observe the prototypical X-ray pulsar Her X-1 and its companion HZ Her. Optical spectra were also obtained contemporaneously at the KPNO 2.1 m. The FOS spectra encompass the 1150-3300 Angstrom range near binary orbital phases 0.5 (X-ray maximum) and at 0.0 (mid-X-ray eclipse). The maximum light spectra show strong, narrow C III N V, O V, Si IV + O IV], N IV], C IV, He II, and N IV emission lines, extending previous IUE results; the O III lambda 3133 Bowen resonance line is also prominent, confirming that the Bowen mechanism is the source of the strong lambda lambda 4640, 4650 emission complex, also seen at maximum light. Most remarkable, however, are the minimum light spectra, where the object is too faint for reasonable observations from IUE. Despite the total eclipse of the X-ray-emitting neutron star, our spectra show strong emission at N V lambda 1240, S IV + O IV] lambda 1400, N IV] lambda 1487, C IV lambda 1549, and He II lambda 4686 (but not the lambda lambda 4640, 4650 complex). Although this hot gas whose emission dominates the UV light at phase 0.0 might be associated with the ''accretion disk corona,'' it is more likely the source is somewhat less hot (but extended) gas above and around the disk, or perhaps circumstellar material such as a stellar wind.