We present and discuss ultraviolet and optical photometry from the Ultraviolet/Optical Telescope, X-ray limits from the X-Ray Telescope on Swift, and imaging polarimetry and ultraviolet/optical spectroscopy with the Hubble Space Telescope, all from observations of ASASSN-15lh. It has been classified as a hydrogen-poor superluminous supernova (SLSN I), making it more luminous than any other supernova observed. ASASSN-15lh is not detected in the X-rays in individual or co-added observations. From the polarimetry we determine that the explosion was only mildly asymmetric. We find the flux of ASASSN-15lh to increase strongly into the ultraviolet, with an ultraviolet luminosity 100 times greater than the hydrogen-rich, ultraviolet-bright SLSN II SN 2008es. We find that objects as bright as ASASSN-15lh are easily detectable beyond redshifts of ~4 with the single-visit depths planned for the Large Synoptic Survey Telescope. Deep near-infrared surveys could detect such objects past a redshift of ~20, enabling a probe of the earliest star formation. A late rebrightening-most prominent at shorter wavelengths-is seen about two months after the peak brightness, which is itself as bright as an SLSN. The ultraviolet spectra during the rebrightening are dominated by the continuum without the broad absorption or emission lines seen in SLSNe or tidal disruption events (TDEs) and the early optical spectra of ASASSN-15lh. Our spectra show no strong hydrogen emission, showing only Ly{alpha} absorption near the redshift previously found by optical absorption lines of the presumed host. The properties of ASASSN-15lh are extreme when compared to either SLSNe or TDEs.