We measure the UV-continuum slope {beta} for over 4000 high-redshift galaxies over a wide range of redshifts z~4-8 and luminosities from the HST HUDF/XDF, HUDF09-1, HUDF09-2, ERS, CANDELS-N, and CANDELS-S data sets. Our new {beta} results reach very faint levels at z~4 (-15.5 mag: 0.006 L_z=3_^*^), z~5 (-16.5 mag: 0.014 L_z=3_^*^), and z~6 and z~7 (-17 mag: 0.025 L_z=3_^*^). Inconsistencies between previous studies led us to conduct a comprehensive review of systematic errors and develop a new technique for measuring {beta} that is robust against biases that arise from the impact of noise. We demonstrate, by object-by-object comparisons, that all previous studies, including our own and those done on the latest HUDF12 data set, suffered from small systematic errors in {beta}. We find that after correcting for the systematic errors (typically {Delta}{beta}~0.1-0.2) all {beta} results at z~7 from different groups are in excellent agreement. The mean {beta} we measure for faint (-18 mag: 0.1L_z=3_^*^) z~4, z~5, z~6, and z~7 galaxies is -2.03+/-0.03+/-0.06 (random and systematic errors), -2.14+/-0.06+/-0.06, -2.24+/-0.11+/-0.08, and -2.30+/-0.18+/-0.13, respectively. Our new {beta} values are redder than we have reported in the past, but bluer than other recent results. Our previously reported trend of bluer {beta}'s at lower luminosities is confirmed, as is the evolution to bluer {beta}'s at high redshifts. {beta} appears to show only a mild luminosity dependence faintward of M_UV, AB_~-19 mag, suggesting that the mean {beta} asymptotes to ~-2.2 to -2.4 for faint z>=4 galaxies. At z~7, the observed {beta}'s suggest non-zero, but low dust extinction, and they agree well with values predicted in cosmological hydrodynamical simulations.