We investigate evolution of clumpy galaxies with the Hubble Space Telescope (HST) samples of ~17,000 photo-z and Lyman break galaxies at z~0-8. We detect clumpy galaxies with off-center clumps in a self-consistent algorithm that is well tested with previous study results, and measure the number fraction of clumpy galaxies at the rest-frame UV, f_clumpy^UV. We identify an evolutionary trend of f_clumpy^UV over z~0-8 for the first time: f_clumpy^UV increases from z~8 to z~1-3 and subsequently decreases from z~1 to z~0, which follows the trend of Madau-Lilly plot. A low average Sersic index of n~1 is found in the underlining components of our clumpy galaxies at z~0-2, indicating that typical clumpy galaxies have disk-like surface brightness profiles. Our f_clumpy^UV values correlate with physical quantities related to star formation activities for star-forming galaxies at z~0-7. We find that clump colors tend to be red at a small galactocentric distance for massive galaxies with log(M_*/M_sun)>~11. All of these results are consistent with a picture that a majority of clumps form in the violent disk instability and migrate into the galactic centers.