We present Hubble Space Telescope and Far Ultraviolet Spectroscopic Explorer observations of the intergalactic absorption toward QSO PG 1116+215 in the 900-3000 ? spectral region. We detect 25 Ly? absorbers along the sight line at rest-frame equivalent widths Wr > 30 m?, yielding (dN/dz)Ly? = 166 ? 20 over an unblocked redshift path ?zLy? = 0.150. Two additional weak Ly? absorbers with Wr ? 15-20 m? are also present. Eight of the Ly? absorbers have large line widths (b 40 km s-1). The detection of narrow O VI absorption in the broad Ly? absorber at z = 0.06244 supports the idea that the Ly? profile is thermally broadened in gas with T > 105 K. We find dN/dz ? 53 for broad Ly? absorbers with Wr 30 m? and b ? 40 km s-1. This number drops to dN/dz ? 40 if the line widths are restricted to 40 ? b ? 100 km s-1. If the broad Ly? lines are dominated by thermal broadening in hot gas, the amount of baryonic material in these absorbers is enormous, perhaps as much as half the baryonic mass in the low-redshift universe. We detect O VI absorption in several of the Ly? clouds along the sight line. Two detections at z = 0.13847 and z = 0.16548 are confirmed by the presence of other ions at these redshifts (e.g., C II-III, N II-III, N V, O I, O VI, and Si II-IV), while the detections at z = 0.04125, 0.05895, 0.05928, and 0.06244 are based upon the Ly? and O VI detections alone. We find (dN/dz) ? 18 for O VI absorbers with Wr > 50 m? toward PG 1116+215. The information available for 13 low-redshift O VI absorbers with Wr ? 50 m? along six sight lines yields (dN/dz) ? 13 and ?b(O ) 0.0022 h, assuming a metallicity of 0.1 solar and an O VI ionization fraction f ? 0.2. The properties and prevalence of low-redshift O VI absorbers suggest that they too may be a substantial baryon repository, perhaps containing as much mass as stars and gas inside galaxies. The redshifts of the O VI absorbers are highly correlated with the redshifts of galaxies along the PG 1116+215 sight line, though few of the absorbers lie closer than ~600?h to any single galaxy. We analyze the kinematics and ionization of the metal-line systems along this sight line and discuss the implications of these observations for understanding the physical conditions and baryonic content of intergalactic matter in the low-redshift universe.