We present FUSE observations of OVI absorption in a sample of 100 extragalactic targets and 2 distant halo stars. We describe the details of the calibration, alignment in velocity, continuum fitting, and manner in which contaminants were removed (Galactic H2, absorption intrinsic to the background target and intergalactic Ly-beta lines). We searched for OVI absorption in the velocity range -1200 to 1200 km/s. With a few exceptions, we only find OVI between -400 and 400 km/s; the exceptions may be intergalactic OVI. We discuss the separation of the observed OVI absorption into components associated with the Galactic halo and components at high-velocity, which are probably located in the neighborhood of the Galaxy. We describe the measurements of equivalent width and column density, and we analyze the different contributions to the errors. We conclude that low-velocity Galactic OVI absorption occurs along all sightlines - the few non-detections only occur in noisy spectra. We further show that high-velocity OVI is very common, having equivalent width >65 mAA in 50% of the sightlines and >30 mAA in 70% of the high-quality sightlines. The high-velocity OVI absorption has velocities relative to the LSR of +/-(100--330) km/s; there is no correlation between velocity and absorption strength. We present 50 km/s wide OVI channel maps. These show evidence for the imprint of Galactic rotation. They also highlight two known HI high-velocity clouds (complex~C and the Magellanic Stream). The channel maps further show that OVI at velocities <-200 km/s occurs along all sightlines in the region l=20-150, b<-30, while OVI at velocities >200 km/s occurs along all sightlines in the region l=180-300, b>20 (abbreviated).
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