Our nation’s first president, George Washington, never aligned with any political party and warned against them in his farewell address to the nation. Ironically, the first political parties came from his advisors, including Alexander Hamilton, James Madison, and Thomas Jefferson. Madison and Jefferson founded the Democratic-Republican party which advocated for a smaller central government, while Alexander Hamilton led the Federalist Party which preferred a strong central government. Later, Andrew Jackson would lead the Jacksonian Democrats, which eventually evolved into the current Democratic Party. Henry Clay would lead their more conservative counterpart, the Whig party. The Whigs collapsed over disagreements over the matter of slavery, and were eventually replaced by the anti-slavery former Whigs that made up the Republican party. Over the years, the names of the major parties did not change, but their policies shifted to adapt to the changing needs of the country.
You can read Washington's Farewell Address at The Avalon Project.
The Library of Congress exhibit on Creating the United States features a section on the formation of political parties.
The American Presidency Project, hosted at the University of California, Santa Barbara, features National Political Party Platforms 1840-present.
The two major political parties in the contemporary United States are the Democrats and the Republicans. The modern-day Democratic party is considered to be more liberal and supports organized labor, better access to healthcare, and righting economic, gender, and racial inequality as its major platforms. The Republican party is thought to be more conservative and focuses on lowering taxes, maintaining the free market, and restricting immigration.
These videos from Vox.com provide information on the various ideological shifts the Democratic and Republican parties experienced over the last few decades.
Many people consider themselves to be “independent” and do not align with any party. The last time a politician not affiliated with the Democratic or Republican party won a presidential election was 1848, while one of the major parties has controlled the House of Representatives and the Senate since 1856. Many third parties exist and have held power on the national and state levels, but none have managed to make a viable attempt to win the U.S. presidency.
Project Vote Smart maintains a list of political parties currently active in the United States.