We compile a complete collection of reliable Hubble parameter H(z) data to redshift z ≤ 2.36 and use them with the Gaussian Process method to determine continuous H(z) functions for various data subsets. From these continuous H(z)'s, summarizing across the data subsets considered, we find H0 ∼ 67 4 km s−1 Mpc−1, more consistent with the recent lower values determined using a variety of techniques. In most data subsets, we see a cosmological deceleration-acceleration transition at 2 significance, with the data subsets transition redshifts varying over at 1 significance. We find that the flat-ΛCDM model is consistent with the H(z) data to a z of 1.5 to 2.0, depending on data subset considered, with 2 deviations from flat-ΛCDM above this redshift range. Using the continuous H(z) with baryon acoustic oscillation distance-redshift observations, we constrain the current spatial curvature density parameter to be , consistent with a flat universe, but the large error bar does not rule out small values of spatial curvature that are now under debate.