We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity functions at z=4-8. We use deep Hubble Space Telescope imaging over the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey/GOODS fields, the Hubble Ultra Deep Field, and the Hubble Frontier Field deep parallel observations near the Abell 2744 and MACS J0416.1-2403 clusters. The combination of these surveys provides an effective volume of 0.6-1.2x10^6^Mpc^3^ over this epoch, allowing us to perform a robust search for faint (M_UV_=-18) and bright (M_UV_<-21) high-redshift galaxies. We select candidate galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 candidate galaxies at 3.5<z<8.5, with >1000 galaxies at z~6-8. We measure both a stepwise luminosity function for candidate galaxies in our redshift samples, and a Schechter function, using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end, our UV luminosity functions agree with previous studies, yet we find a higher abundance of UV-bright candidate galaxies at z>=6.