In the 20th century
1932 and 1980?
1912, because it really marks the beginning of a progressive movement within the Democratic Party. For the first time you had a Democratic regime representing government activism, social reform, a new national reserve bank, and international cooperation. And this from a party still largely rooted in the South. It presaged the rise of the New Deal Coalition, and therefore is to me the dawn of the modern Democratic Party. Wilson is also a pivotal figure, since in my mind the decision to enter into a foreign war was on the level of the Louisiana Purchase and secession as a moment in which the fundamental nature of the republic was irrevocably changed.
1932? Perhaps. One could say FDR saved capitalism from itself. The election of a Democrat was a foregone conclusion, but this particular Democrat was the right person for the job at the most critical juncture of the 20th Century.
1940? We would have entered the war under Wilkie. Maybe sooner than in the OTL.
1968? The Democratic Primary was hugely consequential, though I think the changes happening in the country had little to do with who was in the White House. It did mark the beginning of the end of the New Deal Coalition, which would have huge consequences when it came to the future of the welfare state in America.
1980? The New Right triumphs for the first time. Reagan, his administration, and his allies were responsible for shifting the soul of conservatism away from pro-business elitism to a coalition of moralists and small government activists. This movement had been growing for some time, but Reagan made the New Right a dominant force within American politics like never before. We can thank this election for the current contentious left/right divide.
2000? Technically still in the 20th Century, Bush and his neoconservatives are responsible for the new pro-military, pro-American-power orthodoxy currently dominating White America. A lot of that has to do with 9/11, and who knows what the response would have been under a Gore administration, but I can guarantee you the nation would have taken a radically different path.