Dust-obscured galaxies (DOGs) are a subset of high-redshift (z ≈ 2) optically-faint ultra-luminous infrared galaxies (ULIRGs, e.g., L_(IR) > 10^(12) L_☉). We present new far-infrared photometry, at 250, 350, and 500 μm (observed-frame), from the Herschel Space Telescope for a large sample of 113 DOGs with spectroscopically measured redshifts. Approximately 60% of the sample are detected in the far-IR. The Herschel photometry allows the first robust determinations of the total infrared luminosities of a large sample of DOGs, confirming their high IR luminosities, which range from 10^(11.6) L_☉ 10^(13) L_☉. The rest-frame near-IR (1-3 μm) spectral energy distributions (SEDs) of the Herschel-detected DOGs are predictors of their SEDs at longer wavelengths. DOGs with "power-law" SEDs in the rest-frame near-IR show observed-frame 250/24 μm flux density ratios similar to the QSO-like local ULIRG, Mrk 231. DOGs with a stellar "bump" in their rest-frame near-IR show observed-frame 250/24 μm flux density ratios similar to local star-bursting ULIRGs like NGC 6240. None show 250/24 μm flux density ratios similar to extreme local ULIRG, Arp 220; though three show 350/24 μm flux density ratios similar to Arp 220. For the Herschel-detected DOGs, accurate estimates (within ~25%) of total IR luminosity can be predicted from their rest-frame mid-IR data alone (e.g., from Spitzer observed-frame 24 μm luminosities). Herschel-detected DOGs tend to have a high ratio of infrared luminosity to rest-frame 8 μm luminosity (the IR8 = L_(IR)(8-1000 μm)/νL_ν(8 μm) parameter of Elbaz et al.). Instead of lying on the z = 1-2 "infrared main sequence" of star-forming galaxies (like typical LIRGs and ULIRGs at those epochs) the DOGs, especially large fractions of the bump sources, tend to lie in the starburst sequence. While, Herschel-detected DOGs are similar to scaled up versions of local ULIRGs in terms of 250/24 μm flux density ratio, and IR8, they tend to have cooler far-IR dust temperatures (20-40 K for DOGs versus 40-50 K for local ULIRGs) as measured by the rest-frame 80/115 μm flux density ratios (e.g., observed-frame 250/350 μm ratios at z = 2). DOGs that are not detected by Herschel appear to have lower observed-frame 250/24 μm ratios than the detected sample, either because of warmer dust temperatures, lower IR luminosities, or both
