We report the results of an extensive FUSE study of high velocity OVI absorption along 102 complete sight lines through the Galactic halo. The high velocity OVI traces a variety of phenomena, including tidal interactions with the Magellanic Clouds, accretion of gas, outflow 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 OVI features at velocities of -500 < v(LSR) < +500 km/s along 59 of the 102 sight lines. Approximately 60% of the sky (and perhaps as much as 85%) is covered by high velocity H+ associated with the high velocity OVI. Some of the OVI is associated with known high velocity HI structures (e.g., the Magellanic Stream, Complexes A and C), while some OVI features have no counterpart in HI 21cm emission. The smaller dispersion in the OVI velocities in the GSR and LGSR reference frames compared to the LSR is necessary (but not conclusive) evidence that some of the clouds are extragalactic. Most of the OVI cannot be produced by photoionization, even if the gas is irradiated by extragalactic background radiation. Collisions in hot gas are the primary OVI ionization mechanism. We favor production of some of the OVI at the boundaries between warm clouds and a highly extended [R > 70 kpc], hot [T > 10^6 K], low-density [n < 10^-4 cm^-3] Galactic corona or Local Group medium. A hot Galactic corona or Local Group medium and the prevalence of high velocity OVI are consistent with predictions of galaxy formation scenarios. Distinguishing between the various phenomena producing high velocity OVI will require continuing studies of the distances, kinematics, elemental abundances, and physical states of the different types of high velocity OVI features found in this study. (abbreviated)
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