Spectra of the bright symbiotic star AG Draconis (BD +67°922) in the wavelength range 905-1187 Å obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE) are presented. The spectra show a number of narrow, nebular emission lines, together with a uniform continuum from the hot component of the system, and numerous interstellar absorption lines. We infer the existence of Ne VIII in the AG Dra nebula through the identification of the Ne VII λ973.3 recombination line. The emission-line spectrum is dominated by intense lines of O VI but also shows weaker lines from highly ionized ions including Ne V, Ne VI, S IV, and S VI. Members of the He II Balmer series can be identified up to n=20. Lines of Fe II and Fe III fluoresced by O VI λ1032 are identified at wavelengths 1141.172 and 1142.429 Å, respectively. The emission lines are shown to be produced in a plasma with an electron temperature of 20,000-30,000 K, photoionized by the white dwarf. The Ne VI λ997/λ999 ratio shows that this ion and all others except perhaps Ne VII are formed at least 300 white dwarf radii from the white dwarf. Revised wavelengths for the Ne V 2s22p2 3P0,1-2s2p3 5S2 and Ne VI 2s22p 2P-2s2p2 4P transitions are published.