Hubble Space Telescope Fine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: Period-Luminosity Relations

(abridged) We present new absolute trigonometric parallaxes and relative proper motions for nine Galactic Cepheid variable stars: l Car, zeta Gem, beta 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 with an average sigma_pi/pi = 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_{VI} bandpasses corrected for interstellar extinction and Lutz-Kelker-Hanson bias. Adding our previous absolute magnitude determination for delta 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_$ 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_{VI} identical in the two galaxies within their respective errors. Our data lead to a W_{VI} distance modulus for the Large Magellanic Cloud, m-M = 18.50\pm0.03, uncorrected for any metallicity effects. Applying recently derived metalllcity corrections yields a corrected LMC distance modulus of (m-M)_0=18.40\pm0.05. Comparing our Period-Luminosity relationship to solar-metallicity Cepheids in NGC 4258 results in a distance modulus, 29.28 \pm 0.08, which agrees with that derived from maser studies.