We report results from a Far Ultraviolet Spectrographic Explorer (FUSE) survey of interstellar molecular hydrogen (H_2_) in the Galactic disk toward 139 O-type and early B-type stars at Galactic latitudes |b|<=10{deg}, with updated photometric and parallax distances. H_2_ absorption is measured using the far-UV Lyman and Werner bands, including strong R(0), R(1), and P(1) lines from rotational levels J=0 and J=1 and excited states up to J=5 (sometimes J=6 and 7). For each sight line, we report column densities N_H2_, N_HI_, N(J), and N_H_=N_HI_+2N_H2_ and the molecular fraction f_H2_=2N_H2_/N_H_. Our survey extends the 1977 Copernicus H_2_ survey up to N_H_~5x10^21^cm^-2^. The lowest rotational states have excitation temperatures and rms dispersions <T_01_>=88+/-20K and <T_02_>=77+/-18K, suggesting that J=0, 1, 2 are coupled to the gas kinetic temperature. Populations of higher-J states exhibit mean excitation temperatures <T_24_>=237+/-91K and <T_35_>=304+/-108K, produced primarily by UV radiative pumping. Correlations of f_H2_ with E(B-V) and N_H_ show a transition to f_H2_>=0.1 at N_H_>~10^21^cm^-2^ and E(B-V)>~0.2, interpreted with an analytic model of H_2_ formation-dissociation equilibrium and attenuation of the far-UV radiation field by self-shielding and dust opacity. Results of this disk survey are compared to previous FUSE studies of H_2_ in translucent clouds, at high Galactic latitudes, and in the Magellanic Clouds. Using updated distances to the target stars, we find average sight-line values <f_H2_>=0.20 and <N_H_/E(B-V)>=6.07x10^21^cm^-2^/mag.