We present new statistical parallax solutions for the absolute magnitude and kinematics of RR Lyrae stars. New proper motion, radial velocity, and abundance data are used; the new data set is 50% larger, and of higher quality, than previously available data sets. Based on an a priori kinematic study, we separate the stars into halo and thick disk sub-populations. Statistical parallax solutions on these sub-samples yield M_V(RR) = +0.71 +/- 0.12 at <[Fe/H]> = -1.61 for the halo (162 stars), and M_V(RR) = +0.79 +/- 0.30 at <[Fe/H]> = -0.76 for the thick disk (51 stars). The solutions yield kinematic parameters (solar motion and velocity ellipsoid) in good agreement with estimates of the halo and thick disk kinematics derived from both RR Lyrae stars and other stellar tracers. Monte Carlo simulations indicate that the solutions are accurate, and that the errors may be smaller than the estimates above. The simulations reveal a small bias in the disk solutions, and appropriate corrections are derived. The large uncertainty in the disk M_V(RR) prevents ascertaining the slope of the M_V(RR)-[Fe/H] relation. We find that (1) the distance to the Galactic Center is 7.6 +/- 0.4 kpc; (2) the mean age of the 17 oldest Galactic globular clusters is 16.5 _{-1.9}^{+2.1} Gyr; and (3) the distance modulus of the LMC is 18.28 +/- 0.13 mag. Estimates of H_0 which are based on an LMC distance modulus of 18.50 (e.g., Cepheid studies) increase by 10% if they are recalibrated to match our LMC distance modulus.
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