The Republican and Democratic parties exist due to the strikingly contrasting ethnic and cultural differences of each. Though both parties originally lacked ideological differences, they were clearly separated by difference of beliefs in regards to issues of morality and liberalism.
Democrats believed that the country's government should hold the power to set one concrete moral standard for the entire country. Contrarily, Republicans believed that the government had no place in regulating the moral affairs of society and called for more privacy on such issues.
As religious and moral affairs touched Americans more personally than political matters might have, these differences caused an uproar of passionate competition and resulted in the formation of the Republican and Democratic parties.
It is worth noting that the founding fathers of the United States, especially George Washington, opposed the creation of political parties. Washington felt that political parties were very negative for a democracy. The US Constitution does not mention political parties.
There are two answers to the original question, depending on what the asker was after.
If the answer being sought is "Why is there a Republican Party and a Democratic Party now?" - i.e. why do the US really only have two political parties - the answer lies in the practical consequences of the design of how we elect out representatives.
All Federal elections in the United States are "winner-take-all" - that is, there is only a single office contending in a given election, and the "first-past-the-post" method of voting determines the winner. There is no runoff for candidates who don't get an absolute majority, nor is does the US use any sort of preferential voting system. All that counts in that the winner must get the absolute largest sum of votes of any candidate in that election.
This form of voting means that the only real effective strategy of winning is to have a party which appears to the largest number of voters. There is no benefit in forming alliances with other parties, as only a single winner can be chosen, and votes can't be transferred. Thus, a party should espouse ideas that appeal to a large number of voters, while avoiding those which alienate large numbers. Generally speaking, that means that both parties will try to appeal to the middle 80% of a voter base, ignoring the outer 10% on the political idea spectrum.
This means that there really can be two major parties, since a candidate needs to win the plurality of any election - a party realistically needs to be able to pull at least 40% of the vote to have any say in the Federal government. For example, let's say there are three parties: A which pulls about 45% of the vote, B which pulls 35% of the vote, and C which pulls 20% of the vote, averaged across all individual elections being run. Given that different areas have variable distribution of the above percentages, with winner-take-all elections, that means that the President will always be selected from either A or B, and Congress will most likely consist of at most 5% C, and 55% of A and 40% of B. Thus, while C is reasonably popular, it has virtually no political power.
Also, in the above scenario, party B will find it highly profitable to find the most important issue for party C, and, if that issue isn't objectionable to it's normal membership, start promoting it. It will then be able to co-opt a large percentage of the normal C voters, increasing it's power. By doing this, the actual voting percentage moves to C = 5%, B = 50%, and A = 45%. This leads to a situation where any new idea or political movement is absorbed (and usually heavily moderated) by one of the two major parties.
In addition, the local political process in the USA means that any party requires a very significant political organization to even get on the ballot, and the media generally refuses to give much attention to "fringe" parties, further reinforcing the 2-party system.
If the answer being sought is "Why were the Republican and Democratic Parties formed?" - i.e. what's the history behind the creation of the Republican and Democratic Parties - then a bit of historical background is needed.
The Democratic Party was originally founded as the Democratic-Republican Party in the early 1790s by Thomas Jefferson and James Madison, to oppose the Federalist Party which had been founded a few years earlier by Alexander Hamilton. The D-R Party espoused what are known now as classical Jeffersonian Democracy views - isolationist, pro-agrarian, smaller central government. The Federalists favored a much stronger central government, what would now be called "internationalism", and were more pro-merchant.
The D-R Party ended up splitting into two around the time of the 1824 presidential election; one faction, now called the Democratic Party, supported Andrew Jackson's candidacy, while the other faction, originally called the Republican Party (but soon changed its name to the Whig Party), opposed Jackson. The modern Democratic Party is a direct descendant from this Democratic Party of 1824.
The modern Republican Party is also a descendant of this factionalization of the old D-R Party. In the 1850s, the Whig Party was split over the issue of slavery - in effect a very public North/South split inside the Party. The Northern branch of the Whigs became the Republican Party, with Abraham Lincoln as its first Presidential candidate. The Republican Party received a huge boost in power by being the dominant pro-Union/anti-slavery party of the 1860 election, and thus being the leader of the Union effort in the Civil War.
Answer this question… The Republican party
Democratic party, which replaced the Bull Moose party
The Democratic-Republican Party effectively ended in 1824, when it split into separate factions that eventually became the modern Democratic and Republican parties. However, the transition was not immediate, and it took several years for these new parties to fully crystallize and supplant the Democratic-Republican Party.
democratic, and republican
Republican Party
The Democratic Party and the Republican Party have never been together as a single party.
Monroe belonged to the Democratic-Republican party, the party of Jefferson and Madison.
Democratic-Republican Party was created in 1791.
He was a Democratic-republican. Jefferson and Madison created the Democratic Republican Party to oppose the Federalist Party.
republican and democratic party or the democraric republic
James Madison's political party affiliation was the "Democratic-Republican Party" a party organized by Thomas Jefferson and James Madison. The Democratic and Republican parties as we know them today did not exist at that time. The Republican Party was started in 1860 when a group split off from the Democratic Party which had changed and evolved from the original Democratic-Republican Party.
The Democratic-Republican Party was better known as the Republican Party. The later Republican Party was named to pay homage to this party.
Democratic Leftwing Republican Party was created in 1925.
Croatian Democratic Republican Party was created in 2000.
Croatian Democratic Republican Party ended in 2005.
The modern Democratic Party in the US originated with the Republican Party: now referred to as the Democratic-Republican Party (1791-1825). The Democratic Party was founded in 1828. After the original Democratic-Republican Party split in 1825, those who opposed Democratic president Andrew Jackson formed the Whig Party in 1833.
The Democratic-Republican Party was the forerunner of the Democratic Party. It was started by Thomas Jefferson.