Using UV spectra obtained with FUSE, HST, and/or IUE together with higher resolution optical spectra, we determine interstellar column densities of 12CO, 13CO, and/or C2 for 10 Galactic sight lines with E(B - V) ranging from 0.37 to 0.72. The N(CO)/N(H2) ratio varies over a factor of 100 in this sample, due primarily to differences in N(CO). For a given N(H2 ), published models of diffuse and translucent clouds predict less CO than is observed. The J = 1-3 rotational levels of 12CO are subthermally populated in these sight lines, with Tex typically between 3 and 7 K. In general, there appears to be no significant difference between the excitation temperatures of 12CO and 13CO. Fits to the higher resolution CO line profiles suggest that CO (like CN) is concentrated in relatively cold, dense gas. We obtain C2 column densities from the F-X (0-0) band at 1341 Å (three sight lines; J = 0-12), the F-X (1-0) band at 1314 Å (one sight line; J = 0-12), the D-X (0-0) band at 2313 Å (four sight lines; J = 0-18), and the A-X (3-0) and (2-0) bands at 7719 and 8757 Å (seven sight lines; J = 0-12). Comparisons among those column densities yield a set of mutually consistent band f-values for the UV and optical C2 bands, but also reveal some apparent anomalies within the F-X (0-0) band. Both the kinetic temperature Tk inferred from the C2 rotational populations and the excitation temperature T02(C2) are generally smaller than the corresponding T01(H2)—suggesting that C2 is concentrated in colder, denser gas than H2. Incorporating additional column density data for K I, HD, CH, C2, C3, CN, and CO from the literature (for a total sample of 74 sight lines), we find that (1) CO is most tightly correlated with CN; (2) the ratios 12CO/H2 and 13CO/H2 both are fairly tightly correlated with the density indicator CN/CH (but C2/H 2 is not); and (3) the ratio 12CO/13CO is somewhat anticorrelated with both CN/CH and N(CO). Sight lines with 12CO/13CO below the average local Galactic value of 12C/13C appear to sample colder, denser gas in which isotope exchange reactions have enhanced 13CO, relative to 12CO.