Laser-ablated tungsten atoms react with molecular hydrogen upon condensation in excess neon. The tungsten hydrides WH, WH2, WH3, WH4, and WH6 are identified by isotopic substitution (D-2, HD) and by density functional theory calculations of vibrational fundamentals. The WH diatomic gives a 1860.2 cm(-1) band, WH2 gives a strong 1831.9 cm(-1) absorption, and WH3 gives a sharp 1894.6 cm(-1) peak. Absorptions due to WH4 appear at 1920.1 and 525.2 cm(-1), increase on annealing in solid neon, and support a tetrahedral structure. Sharp new absorptions at 2021.2, 2004.4, 1953.8, 1927.5, 1080.3, and 840.7 cm(-1) are assigned to WH6, based on deuterium isotopic shifts and comparison with frequencies computed by DFT for the distorted trigonal prism structure predicted earlier to be the global minimum energy structure for WH6. The bands of WH6 increase on annealing, decrease on broadband photolysis, and restore on further annealing. This is the first experimental identification of the WH2, WH4, and WH6 hydride molecules, and WH6 is the only known neutral metal hexahydride.