We report the results of a FUSE study of high velocity O vi absorption along complete sight lines through the Galactic halo in directions toward 100 extragalactic objects and 2 halo stars . The high velocity O vi traces a variety of phenomena , including tidal interactions with the Magellanic Clouds , accretion of gas , outflowing material from the Galactic disk , warm/hot gas interactions in a highly extended Galactic corona , and intergalactic gas in the Local Group . We identify 85 high velocity O vi features at \geq 3 \sigma confidence at velocities of -500 < v _ { LSR } < +500 km s ^ { -1 } . There are an additional 6 confirmed or very likely ( > 90 % confidence ) features plus 2 tentative detections between v _ { LSR } = +500 and +1200 km s ^ { -1 } ; these very high velocity O vi features trace intergalactic gas beyond the Local Group . The 85 O vi features have velocity centroids ranging from -372 \lesssim \bar { v } _ { LSR } \lesssim - 90 km s ^ { -1 } to +93 \lesssim \bar { v } _ { LSR } \lesssim + 385 km s ^ { -1 } , line widths b \sim 16 - 81 km s ^ { -1 } with an average of \langle b \rangle = 40 \pm 14 km s ^ { -1 } , and an average O vi column density \langle \log N \rangle = 13.95 \pm 0.34 with a median value of 13.97 . Values of b greater than the 17.6 km s ^ { -1 } thermal width expected for O vi at T \sim 3 \times 10 ^ { 5 } K indicate that additional non-thermal broadening mechanisms are common . The O vi \lambda 1031.926 absorption is detected at \geq 3 \sigma confidence along 59 of the 102 sight lines surveyed . The high velocity O vi detections indicate that \sim 60 % of the sky ( and perhaps as much as \sim 85 % , depending on data quality considerations ) is covered by high velocity H ^ { + } associated with the O vi . N ( { H } ^ { + } ) \gtrsim 4 \times 10 ^ { 16 } cm ^ { -2 } if the high velocity hot gas has a metallicity similar to that of the Magellanic Stream . About 30 % of the sky is covered by the hot , high velocity H ^ { + } at a level of N ( { H } ^ { + } ) \gtrsim 4 \times 10 ^ { 17 } cm ^ { -2 } , which is similar to the detection rate found for H i 21 cm emission produced by warm neutral gas at a comparable column density level . Some of the high velocity O vi is associated with known H i structures ( the Magellanic Stream , Complex A , Complex C , the Outer Spiral Arm , and several discrete H i HVCs ) . Some of the high velocity O vi features have no counterpart in H i 21 cm emission , including discrete absorption features and positive velocity absorption wings extending from \sim 100 to \sim 300 km s ^ { -1 } that blend with lower velocity absorption produced by the Galactic thick disk/halo . The discrete features may typify clouds located in the Local Group , while the O vi absorption wings may be tidal debris or material expelled from the Galactic disk . Most of the O vi features have velocities incompatible with those of the Galactic halo , even if the halo has decoupled from the underlying Galactic disk . The reduction in the dispersion about the mean of the high velocity O vi centroids when the velocities are converted from the LSR to the GSR and LGSR reference frames is necessary ( but not conclusive ) evidence that some of the clouds are located outside the Galaxy . Most of the O vi can not be produced by photoionization , even if the gas is irradiated by extragalactic ultraviolet background radiation . Several observational quantities indicate that collisions in hot gas are the primary ionization mechanism responsible for the production of the O vi . These include the ratios of O vi column densities to those of other highly ionized species ( C iv , N v ) and the strong correlation between N ( O vi ) and O vi line width . Consideration of the possible sources of collisional ionization favors production of some of the O vi at the boundaries between cool/warm clouds of gas and a highly extended ( R \gtrsim 70 kpc ) , hot ( T > 10 ^ { 6 } K ) , low-density ( n \lesssim 10 ^ { -4 } -10 ^ { -5 } cm ^ { -3 } ) Galactic corona or Local Group medium . The existence of a hot , highly extended Galactic corona or Local Group medium and the prevalence of high velocity O vi are consistent with predictions of current galaxy formation scenarios . Distinguishing between the various phenomena producing high velocity O vi in and near the Galaxy will require continuing studies of the distances , kinematics , elemental abundances , and physical states of the different types of high velocity O vi found in this study . Descriptions of galaxy evolution will need to account for the highly ionized gas , and future X-ray studies of hot gas in the Local Group will need to consider carefully the relationship of the X-ray absorption/emission to the complex high velocity absorption observed in O vi .