We describe a moderate-resolution FUSE mini-survey of H _ { 2 } in the Milky Way and Magellanic Clouds , using four hot stars and four AGN as background sources . FUSE spectra of nearly every stellar and extragalactic source exhibit numerous absorption lines from the H _ { 2 } Lyman and Werner bands between 912 and 1120 Å . One extragalactic sightline ( PKS 2155-304 ) with low N ( H I ) shows no detectable H _ { 2 } , and could be the “ Lockman Hole of molecular gas ” , of importance for QSO absorption-line studies . We measure H _ { 2 } column densities in low rotational states ( J = 0 and 1 ) to derive rotational and/or kinetic temperatures of diffuse interstellar gas . The higher- J abundances can constrain models of the UV radiation fields and gas densities . In three optically thick clouds toward extragalactic sources , we find n _ { H } \approx 30 - 50 cm ^ { -3 } and cloud thicknesses \sim 2 - 3 pc . The rotational temperatures for H _ { 2 } at high Galactic latitude , \langle T _ { 01 } \rangle = 107 \pm 17 K ( seven sightlines ) and 120 \pm 13 K ( three optically thick clouds ) , are higher than those in the Copernicus sample composed primarily of targets in the disk . We find no evidence for great differences in the abundance or state of excitation of H _ { 2 } between sight lines in the Galaxy and those in the SMC and LMC . In the future , we will probe the distribution and physical parameters of diffuse molecular gas in the disk and halo and in the lower-metallicity environs of the LMC and SMC .