With George Washington having been unanimously elected twice in 1789 and 1792, he's always been associated with no political party. It can be argued that he leaned toward the Federalists rather than Jefferson's anti-federalists. But he was above all that, except by the end of his term it was getting politically heated. He warned famously in his farewell address to avoid political factions. Eventually a two-party political system would form and evolve over the course of U.S. political history. With Vice President John Adams' victory in 1796, Federalists remained in power. The only Federalist to be elected president.
In 1800, the country would experience the first change in power from one political faction to another. With Vice President Thomas Jefferson's victory in the election, which had to be decided in the House of Representatives because of a tie vote with Aaron Burr his supposed-to-be-running-mate, Jefferson brought to power his anti-federalist group which became known as the Democratic-Republicans. They would defeat every Federalist candidate in the elections from 1804-1824. That's 7 election wins. The 1820, the Era of Good Feelings was good because there was no opposition party. The Federalists were not a threat to James Monroe's reelection. He won all the electoral votes except one, so that Washington would remain the only president unanimously elected. Since there was no opposition, in 1824 four candidates ran for president as a Democratic-Republican. In that election, Andrew Jackson would receive a plurality of both popular and electoral votes, but with no clear majority the House of Representatives would decide. Secretary of State John Quincy Adams, son of the 2nd POTUS, would be the winner in the House.
Jackson would campaign against the administration for the next four years and in a rematch in 1828 defeat President Adams, who ran as a National Republican. The next elections from 1832 until 1852, the new Democratic Party would go up against the Whigs. The Whig Party would win only 2 elections, 1840 and 1848.
Starting in 1856, the Democrats would face a new political party, the Republican Party. The Democrats would win 22 elections between 1828 and 2012, while the GOP would win 23 elections starting in 1860 through 2004. Yes, 23 is a bigger number than 22, but 3 of the elections that the GOP won actually had the Democratic nominee winning the popular vote in 1876, 1888, and 2000. So it can be said that the Democrats won the popular vote 25 times to the Republican's 20 wins in the popular vote. But like the Constitution says, it's the Electoral College winner that wins the presidency. 23-22.