These are mostly years in which a surprising number of important things happened. For the most part, wars are excluded. Go ahead and argue with my choices in comments.
1687: Isaac Newton invents physics.
1776: American Revolution, Wealth of Nations, first commercial Watt steam engine, Decline and Fall of the Roman Empire.
1789: French Revolution, first American president, Bill of Rights proposed.
1831: HMS Beagle, Faraday's dynamo, Garrison's Liberator, Hunchback of Notre Dame.
1848: Communist Manifesto, gold discovered in California, Seneca Falls, Revolutions of 1848.
1859: Suez canal, Origin of Species, first American oil well, Tale of Two Cities, Riemann Hypothesis, On Liberty.
1900: Quantum mechanics, Interpretation of Dreams, ABO blood typing system, Wizard of Oz, premiere of Tosca.
1905: Albert Einstein's annus mirabilis.
1928: Penicillin, Coming of Age in Samoa, River Rouge plant completed, Passion of Joan of Arc, Mickey Mouse, OED, first regular TV broadcast, All Quiet on the Western Front, sliced bread (against which all future inventions would be compared).
1939: Gone with the Wind, The Wizard of Oz, Stagecoach, Mr. Smith Goes to Washington, Goodbye Mr. Chips, The Rules of the Game, nuclear fission, Batman, World War II, first televised baseball game, first published stories by Isaac Asimov and Robert Heinlein.
1958: First credit card, DARPA, integrated circuit, NASA, USS Nautilus, laser, first communications satellite, first transatlantic jet service.
1969: First human on the moon, Boeing 747, Stonewall, Woodstock, Miracle Mets, ARPANET, Unix, Abbey Road.