Cambrian (14.7%): Undisputed winner, of course: the time in which the major phyla of the animal kingdom took shape, the time of Anomalocaris, Opabinia, and all other weird arthropods and quasi-arthropods roamed the shallow seas. The crucible of animal life, seminal for all that came later.
Cretaceous (11.9%): The absolute peak of megafauna in Earth's history, the time when animals twice as heavy as a fully-grown elephant still felt the need of an armor so thick it covered their eyelids. The time when life on Earth was at its most Most, and ending with the worst single day in its history too. (And also the time when flower plants, spiny-finned fish, and social insects filled the world, but seriously, who has the heart to ignore the giant dinosaurs?)
Ordovician (9.6%): Even though this was my vote, I was surprised to see it rank so high! (The first day, it was enck-to-neck with the Cretaceous!) Most summaries of the history of life don't even mention it by name. This is the Cambrian's younger, less cool but harder-working sibling, the time when animal life detached from the seafloor and filled the waters. Giant nautiloids, swimming trilobites, and the first (jawless) fish.
Jurassic (9.6%): Most of what I said of the Cretaceous also apply here. If you like giant sauropods and stegosaurs more than hadrosaurs and ceratopsians, or think that Tyrannosaurus is too mainstream and Allosaurus deserves more love, the Jurassic -- time of dinosaurs par excellence -- is right there.
Quaternary (9.6%): The Cenozoic in general ranks pretty low -- too normal-looking I guess, we have birds and mammals already -- but the Quaternary stands far above the other two. I suppose Ice Age megafauna still retains its charm!
Devonian (8.8%): Ah, the golden age of fish diversity, the time when the land turned green and our ancestors left the ocean behind. Also the last jawless fish and trilobites had a really good time (the Permian extinction would only mop up the survivors). And the only period placoderms, taken out so soon, were given to shine.
Silurian (7.9%): The time of the very first land ecosystems... if they weren't already around in the Ordovician. Kind of a filler period, by comparison with the Ordovician and the Devonian. Heterostracan fish and sea scorpions are so cool, though.
Carboniferous (6.8%): The great swampy coal forests and their fauna of man-sized quasi-millipedes, raven-sized quasi-dragonflies, and giant armored amphibians is not quite as popular, however. I can't blame people for not caring much for coal anymore, I guess.
Paleogene (6.6%): The quiet time of respite after the downfall of dinosaurs, tropical jungles almost reaching the poles, and the first spread of primates while continents finally took their familiar arrangement. The Cenozoic is not so hot in general, it seems. (Will anyone appreciate the volcanic lake occasionally killing everything in its surroundings and creating one of the best fossil sites on Earth?)
Triassic (6.5%): Triassic fauna is really underappreciated, if you ask me. Long-necked Tanystropheus and flat-toothed placodonts and chameleon-like drepanosaurs, and a profusion of quasi-crocodiles, and the dawn of mammals and dinosaurs, compressed in a brief respite between two mass extinctions.
Permian (5.4%): Poor Permian. No love for the kingdom of synapsids -- sail-backed pelycosaurs and dagger-toothed gorgonopsian -- dethroned by two mass extinctions, and who would have to live in the shade of dinosaurs before resurging in the form of mammals? For Pangea stretching its burning desert heart from pole to pole? For Earth's most terrible mass extinction, that almost took out insects? Someone has to be near the bottom, I guess.
Neogene (2.6%): And there is the actual bottom. Dear Miocene, the golden age of apes and elephants, the time when a world of jungles became the world of woodlands and grasslands that we know today, too familiar to be popular and without the appeal of the Ice Age, someone had to be here.
(Picture credits: Cambrian, Devonian, Permian, Triassic, Jurassic, Neogene, Quaternary by Mark Witton; Carboniferous by Olorotitan; Cretaceous by Gogosardina; Paleogene by Raul Martin, kindly collected by Worldbuilding Pasta; Ordovician, Silurian from Ocean of Origins)