We report the discovery of four transiting extrasolar planets (HAT-P-34b-HAT-P-37b) with masses ranging from 1.05 to 3.33 M J and periods from 1.33 to 5.45 days. These planets orbit relatively bright F and G dwarf stars (from V = 10.16 to V = 13.2). Of particular interest is HAT-P-34b which is moderately massive (3.33 M J), has a high eccentricity of e = 0.441 ± 0.032 at a period of P = 5.452654 ± 0.000016 days, and shows hints of an outer component. The other three planets have properties that are typical of hot Jupiters. Based in part on observations obtained at the W. M. Keck Observatory, which is operated by the University of California and the California Institute of Technology. Keck time has been granted by NOAO (A289Hr) and NASA (N167Hr and N029Hr). Based in part on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. Based in part on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.
