The XRT is a sensitive, autonomous X-ray imaging spectrometer onboard the Swift Gamma-Ray Burst Observatory. The unique observing capabilities of the XRT allow it to autonomously refine the Swift BAT positions (~1-4' uncertainty) to better than 2.5 arcsec in XRT detector coordinates, within 5 seconds of target acquisition by the Swift Observatory for typical bursts, and to measure the flux, spectrum, and light curve of GRBs and afterglows over a wide dynamic range covering more than seven orders of magnitude in flux (62 Crab to < 1 mCrab). The results of the rapid positioning capability of the XRT are presented here for both known sources and newly discovered GRBs, demonstrating the ability to automatically utilise one of two integration times according to the burst brightness, and to correct the position for alignment offsets caused by the fast pointing performance and variable thermal environment of the satellite as measured by the Telescope Alignment Monitor. The onboard results are compared to the positions obtained by groundbased follow-up. After obtaining the position, the XRT switches between four CCD readout modes, automatically optimising the scientific return from the source depending on the flux of the GRB. Typical data products are presented here.