THE MOST METAL-POOR STARS. II. CHEMICAL ABUNDANCES OF 190 METAL-POOR STARS INCLUDING 10 NEW STARS WITH [Fe/H] <=-3.5

We present a homogeneous chemical abundance analysis of 16 elements in 190 metal-poor Galactic halo stars (38 program and 152 literature objects). The sample includes 171 stars with [Fe/H] <= -2.5, of which 86 are extremely metal poor, [Fe/H] <= -3.0. Our program stars include 10 new objects with [Fe/H] <= -3.5. We identify a sample of normal metal-poor stars and measure the trends between [X/Fe] and [Fe/H], as well as the dispersion about the mean trend for this sample. Using this mean trend, we identify objects that are chemically peculiar relative to normal stars at the same metallicity. These chemically unusual stars include CEMP-no objects, one star with high [Si/Fe], another with high [Ba/Sr], and one with unusually low [X/Fe] for all elements heavier than Na. The Sr and Ba abundances indicate that there may be two nucleosynthetic processes at lowest metallicity that are distinct from the main r-process. Finally, for many elements, we find a significant trend between [X/Fe] versus T-eff, which likely reflects non-LTE and/or three-dimensional effects. Such trends demonstrate that care must be exercised when using abundance measurements in metal-poor stars to constrain chemical evolution and/or nucleosynthesis predictions.