We have measured the water and hydrogen outgassing rates of seven vacuum chambers of identical geometry but constructed of different materials and heat treatments. Chambers of five different materials were tested: 304L, 316L, and 316LN stainless steels; titanium (ASTM grade 2); and 6061 aluminum. In addition, chambers constructed of 316L and 316LN stainless steel were subjected to a vacuum-fire process, where they were heated to approximately 950 {deg}C for 24 hours while under vacuum; these two chambers are designated as 316L-XHV and 316LN-XHV. All chambers were of identical geometry and made by the same manufacturer, thus a relative comparison of the outgassing rates among these chambers can be made. Water outgassing rates were measured as a function of time using the throughput technique. The water outgassing results for the 316L, 316LN, 316L-XHV, 316LN-XHV were all similar, but lower than those of 304L by a factor of 3 to 5 lower at 10^4 s. The water outgassing results for Ti and Al chambers were close to that of 304L, Ti being slightly lower. Hydrogen outgassing rates were measured using the rate-of-rise method and performed after a low-temperature bake of 125 {deg}C to 150 {deg}C for a minimum of 72 hours. The Ti, Al, 316L-XHV, and 316LN-XHV chambers all have specific outgassing rates below 1 X 10^-11 Pa L s^-1 cm^-2 and are at least a factor of 100 or better than the 304L chamber. The 304L, 316L, and 316LN chambers without vacuum-fire heat treatment have larger hydrogen outgassing rates than the other chambers, with specific outgassing rates ranging between 4.0 X 10^-11 Pa L s^-1 cm^-2 and 8.0 X 10^-11 Pa L s^-1 cm^-2. We conclude that Ti, Al, 316L-XHV, and 316LN-XHV have hydrogen outgassing rates that make them excellent choices for ultra-high vacuum (UHV) and extreme-high vacuum (XHV) applications, the choice depending on cost and other material properties.