We report new and archival IUE SWP spectra for nine nearby radio galaxies (V < 15 mag), together with optical emission-line data for these galaxies as well as a number of candidates with weaker line emission. We examine both their UV line and continuum properties, as well as their UV and UV-optical line ratios. We find that: 1. Ly-alpha emission is common among local radio galaxies, at modest luminosities (typically 10(41-42) ergs s-1). No apparent relation is found between L(Ly-alpha) and radio power for the nearby radio galaxies alone. Incorporating the known powerful high-redshift radio galaxies, a regression is seen suggesting that L(Ly-alpha) is-proportional-to (P1.4 GHz)0.6 +/- 0.15, with an rms scatter approximately 0.5 dex. We address the reality of this relationship, and discuss its possible consequences. 2. The Ly-alpha/H-alpha ratio in low power nearby radio galaxies is 2-5 times lower than the prediction for case B recombination. Destruction of Ly-alpha photons by grains during resonant scattering can explain the observed deficiency for reasonable metallicities. The role of internal reddening is likely to be small, since the continuum shapes do not allow enough reddening to affect Ly-alpha so strongly. 3. The nearby radio galaxies have in general a small C IV/Ly-alpha ratio (< 0.1). Their narrow line W-lambda(Ly-alpha) values are in the range 20-200 angstrom. Comparison of the C IV and Ly-alpha strengths with those in luminous active nuclei (e.g., Seyferts) suggests that most of the UV continuum comes from the stellar population, and not from the AGN. Most (4/5) of our nearby radio galaxies show an upturn in the continuum below 1450 angstrom, which is found in only 36% (9/25) of the nearby radio-quiet early type galaxies, and not seen in high-redshift radio galaxies. Before a detailed comparison between high- and low-redshift galaxies can be made, UV spectroscopy is needed for substantial numbers of intermediate redshift galaxies (0.1 less-than-or-similar-to z less-than-or-similar-to 1.5) of moderate radio power to address the continuity in the radio galaxy population. This can now be done with HST.