High-ionization forbidden lines from Ca VII, Fe VII, Mg V, Mg VI, Mg VII, and Si VII are found in recent Hubble Space Telescope STIS ultraviolet spectra of the symbiotic star AG Draconis. These species have ionization potentials between 99 and 205 eV, which are unexpected due to the high density (~1010 cm-3) of the AG Dra nebula. The identification of the Mg VII λλ2510, 2629 lines is the first in astrophysical or laboratory spectra, and revised rest wavelengths are suggested from the STIS spectra. Plasma diagnostics from Mg V-VII are applied, but do not provide a consistent constraint on temperature or density. A density >=108 cm-3 is confirmed, however. The lines show double-peaked profiles with widths ~100-160 km s-1, suggestive of an origin in an accretion disk. However, the line widths, if identified with motion in a Keplerian disk, indicate radii much smaller than sizes inferred from the line fluxes themselves. The source of these high-ionization forbidden lines remains unidentified.