The American party system has generally always been a two-party system, especially at the national level. This kind of system ensures that minority viewpoints can’t control the government. There are no actual explicit legal prohibitions against third parties in America, but most governmental institutions require a plurality, and that has generally resulted in two-party domination. The actual parties in control have changed several times over the course of history, and currently they are the Democrats and the Republicans.
Some people are strongly opposed to the American party system because it has the potential to slow down progress. It can sometimes take significant time for a plurality of the populace to embrace new ideas, and with the two-party system, only the two most mainstream viewpoints are often considered on any given issue. At times, ideas that might otherwise become popular may have a difficult time getting any traction or debate, especially if they don’t have enough initial acceptance.
In historical times, there have been short-term third party movements, but it is generally difficult for them to gain a foothold. On the state level, there have been situations where a single party gains control for short periods of time, and other situations where three parties have been in control temporarily. Every once in a while, a single individual from a third party will gain an important national elected position, but it rarely translates to success for that party across the rest of the government.
The first American party system involved the Republicans of Thomas Jefferson’s time and a party called the Federalists. The Republicans were interested in states' rights and individual freedom. The Federalists believed in a strong central government and using government power to maintain control over the populace. On the foreign policy front, the Republicans favored keeping a good relationship with the French, while the Federalists were sympathetic to Britain.
Those parties eventually died and were replaced in the early 1800s by the second American party system involving the Democrats and the Whigs. At that time, the Democrats were basically conservative and populist. They favored states' rights and old-fashioned values. The Whigs were the party of strong governmental power and progressive thought, or the equivalent in that time. They also sometimes favored restricting individual freedoms through alcohol bans.
In the mid-1800s during the ramp up to the Civil War, there was a total breakdown of the party system followed by a short period of chaos. At the end of that period, the remaining parties were the Democrats and the Republicans, which have been the two parties ever since. In those days, the Republicans were the party opposed to slavery, while the Democrats were the party in favor of it, and this was the main thing that separated the two. Over time, these parties have changed and evolved in many different ways.
In the current American party system, the Democrats are the party of liberal thought. They tend to favor things like social programs, financial regulation, and strict enforcement of civil rights. The Republicans are the party of small government and conservative thought. They generally favor states' rights, low taxes, and maintenance of a strong military. When it comes to social issues, the roles are often reversed, with the Democrats favoring lessened government involvement, while the Republicans often favor a more active government role in maintaining traditional values.