We present a detailed dynamical study of the old (7 Gyr) open cluster NGC 188. Our combined radial-velocity data set spans a baseline of 35 years, a magnitude range of 12 ≤ V ≤ 16.5, and a 1° diameter region on the sky. Our magnitude limits include solar-mass main-sequence stars, subgiants, giants, and blue stragglers, and our spatial coverage extends radially to 11.5 core radii. We have measured radial velocities for 1014 stars in the direction of NGC 188 with a precision of 0.4 km s−1, and have calculated radial-velocity membership probabilities for stars with ≥ 3 measurements. We find 420 stars to be high-probability cluster members, including 137 spectroscopic binaries. These detectable binaries all have orbital periods of less than 104 days, and thus are hard. We have derived orbit solutions for 67 member binary stars, and use our 35 main-sequence binaries with orbit solutions to compare the eccentricity and period distributions with simulated observations of the Hurley et al. (2005) model of M67 (4.5 Gyr). We also compare the spatial distributions of cluster member populations.