We have made high signal-to-noise spectroscopic observations of seven radio-loud quasars with the Faint Object Spectrograph on the Hubble Space Telescope and from the ground at McDonald Observatory and at Kitt Peak National Observatory. The resolution is 300-400 km s-1 over the wavelength range 1000-8500 Å, enabling us to separate the broad and narrow components of the emission lines. This is the first study of the optical and UV narrow lines in such high-luminosity active galactic nuclei (AGNs). The most important and striking observational result is the relative weakness of the narrow ultraviolet lines, assuming that they have the same widths as the narrow [O III] λ5007 emission lines. We do not have a single definite detection of a narrow UV line in any of the seven quasars. We have measured all the strong optical narrow lines and have derived upper limits to the strengths of narrow lines in the UV. The latter are much weaker than predicted by dust-free photoionization models and also weaker than those typically seen in Seyfert 2 galaxies and narrow-line radio galaxies. There is direct evidence for the presence of dust with significant reddening, typically E(B-V) ∼ 0.5. A comparison of our sample with the previously observed Seyfert 2s (Kinney et al.) shows that two explanations for the reddening are needed. One is simple foreground reddening, presumably in the host galaxy. However some narrow-line spectra show an unsually weak Lyα/Hβ intensity ratio, but apparently case B hα/Hβ. We interpret this as the result of dust inside the narrow line clouds and show model calculations to support this claim. These and other calculations presented in this paper are used to argue that much of the narrow-line region in the high-luminosity objects lies well beyond the nucleus.