This paper discusses the optical spectroscopic properties of the IRAS 1-Jy sample of ultraluminous infrared galaxies (ULIGs). One hundred and eight of the 118 1-Jy ULIGs have been observed at dlambda = 8.3 AA resolution over the wavelength range ~4500 A -- 8900 A. These data are combined with large, previously published sets of optical spectroscopic data of lower luminosity infrared galaxies to look for systematic trends with infrared luminosity over the luminosity range L_ir ~ 10^{10.5}-10^{13} L_sun. As found in previous studies, the fraction of Seyfert galaxies among luminous infrared galaxies increases abruptly above L_ir ~ 10^{12.3} L_sun --- about 50% of the galaxies with L_ir > 10^{12.3} L_sun present Seyfert characteristics. Many of the optical and infrared spectroscopic properties of the Seyfert galaxies are consistent with the presence of a genuine active galactic nucleus (AGN). About 30% of these galaxies are Seyfert 1s with broad-line regions similar to those of optical quasars. The percentage of Seyfert 1 ULIGs increases with infrared luminosity, contrary to the predictions of the standard unification model for Seyfert galaxies. Comparisons of the broad-line luminosities of optical and obscured Seyfert 1 ULIGs with those of optically selected quasars of comparable bolometric luminosity suggest that the dominant energy source in most of these ULIGs is the same as in optical quasars, namely mass accretion onto a supermassive black hole, rather than a starburst. These results are consistent with recently published ISO, ASCA, and VLBI data. (abridged)

Text and 23 figures (45 pages), Tables 1 - 6 (16 pages)