We present new absolute trigonometric parallaxes and relative proper motions for nine Galactic Cepheid variable stars: ℓ Car, ζ Gem, β Dor, W Sgr, X Sgr, Y Sgr, FF Aql, T Vul, and RT Aur. We obtain these results with astrometric data from Fine Guidance Sensor 1r, a white-light interferometer on Hubble Space Telescope. We find absolute parallaxes in milliseconds of arc: ℓ Car, 2.01 ± 0.20 ; ζ Gem, 2.78 ± 0.18 ; β Dor, 3.14 ± 0.16 ; W Sgr, 2.28 ± 0.20 ; X Sgr, 3.00 ± 0.18 ; Y Sgr, 2.13 ± 0.29 ; FF Aql, 2.81 ± 0.18 ; T Vul, 1.90 ± 0.23 ; and RT Aur, 2.40 ± 0.19 , an average σ π /π = 8%. Two stars (FF Aql and W Sgr) required the inclusion of binary astrometric perturbations, providing Cepheid mass estimates. With these parallaxes we compute absolute magnitudes in V, I, K, and Wesenheit W V I bandpasses corrected for interstellar extinction and Lutz-Kelker-Hanson bias. Adding our previous absolute magnitude determination for δ Cep, we construct Period-Luminosity relations for ten Galactic Cepheids.We compare our new Period-Luminosity relations with those adopted by several recent investigations, including the Freedman and Sandage H 0 projects. Adopting our Period-Luminosity relationship would tend to increase the Sandage H 0 value, but leave the Freedman H 0 unchanged. Comparing our Galactic Cepheid PLR with those derived from LMC Cepheids, we find the slopes for K and W V I identical in the two galaxies within their respective errors. Our data lead to a W V I distance modulus for the Large Magellanic Cloud, m-M = 18.50±0.03, uncorrected for any metallicity effects. Applying recently derived metalllcity corrections yields a corrected LMC distance modulus of (m-M) 0 =18.40±0.05. Comparing our Period-Luminosity relationship to solar-metallicity Cepheids in NGC 4258 results in a distance modulus, 29.28 ± 0.08, which agrees with that derived from maser studies.