In an effort to better understand the UV properties of ultraluminous infrared galaxies (ULIGs), and compare them to the rest-frame UV properties of high redshift submillimeter and Lyman-break galaxies, we have obtained far- and near-UV imaging observations (λeff = 1457 and 2364 Å, respectively) of two luminous infrared galaxies (LIGs-VV 114 and IC 883) and five ULIGs (IRAS 08572+3915, Mrk 273, IRAS 15250+3609, Arp 220, and IRAS 19254-7245) using the Hubble Space Telescope. All the galaxies were detected in both channels. UV light, both diffuse and from star clusters, can be traced to within the inner kilo-parsec of the dominant near-IR nuclei. However, in general, the brightest UV sources are clearly displaced from the I-band and near-IR peaks by at least hundreds of parsecs. Furthermore, only 0.07%-7.3% of the total near-UV light is projected within the inner 500 pc radius, even though this is the same region where most of the bolometric energy is generated. All nuclei are highly obscured by dust. Even after correction for dust reddening, the global UV emission fails to account for the total bolometric luminosities of these systems by factors of 3-75. The discrepancy is much worse if only the central regions, where the bolometric luminosities are generated, are included. In two cases (VV 114 and IRAS 08572+3915), the merging companion galaxies are more prominent in the UV than the more IR luminous member. While all our galaxies show possible signatures of active galactic nucleus (AGN) activity, only IRAS 19254-7245 yields even a possible detection of an AGN in our UV images. Simple calculations show that all but one of our galaxies would be expected to drop below the detection thresholds of, e.g., the Hubble Deep Fields at redshifts between 1.5 and 3, and we find that ∼2 of our five ULIGs would be selected as extremely red objects in this redshift range. A typical ULIG in our sample would be too faint to be detected at high redshift in the deepest current optical or submillimeter deep surveys. Only VV 114 has UV luminosity and color similar to Lyman-break galaxies at z ∼ 3; the other galaxies would be too faint and/or red to be selected by current surveys. The low UV brightnesses of our ULIGs mean that they would not appear as optically bright (or bright ERO) submillimeter galaxy counterparts, although they might be similar to the fainter submillimeter galaxy counterparts.