The Democratic Party has its origins in the anti-Federalist party established in the first few years of the United States' existence. Thomas Jefferson was the leader of this group, arguing against the strong centralized government put forth by Alexander Hamilton and the leaders of the first administration. This group eventually began calling themselves the Democratic Republicans. With Jefferson and James Madison at the helm, the party grew; Jefferson's presidency in 1800 further solidified the party. The party was kept in the executive branch until 1824 by a coalition of Northern urbanites and Southern farmers. The Democratic Republicans were such a dominating force the Federalists dissolved and politics in the US became infighting within the Democratic Republicans.
Andrew Jackson's administration from 1828 to 1836 finally solidified the opposition to the Democratic Party (and was the period where the party finally simplified its name). The Whig party was formed primarily as an anti-Jackson party. This party had a tenuous existence however, winning only two presidential elections; it ultimately dissolved after the election of 1852. However, the opposition to the Democrats remained, centering on the divisive slavery issue. This opposition coalesced once more, forming the Republican Party in 1854. The Democrats, dividing their ticket between two candidates over the issue of slavery in the territories, made Republican Abraham Lincoln's 1860 victory an easy one. After the Civil War, Republicans were able to paint the Democrats as the party of the South -- and therefore the party of rebellion -- and take much of the power in the US throughout the last half of the 1800s. The Democrats finally won a presidential election in 1912, primarily because Theodore Roosevelt, running on the Progressive Party ticket, split the Republican vote.
The Democrats finally began regaining ground during the Great Depression. The incompetence of Republican Herbert Hoover helped sweep Franklin D. Roosevelt and the new reform-oriented Democrats into power. They pulled the country out of the depression through massive government spending in public works. They retained the presidency until Eisenhower's victory in 1952. John F. Kennedy retook the presidency for the Democrats; after his assasination Lyndon Johnson spent his administration passing social welfare and civil rights legistlation; however, the combination of the Vietnam War and George Wallace's third-party run poisoned the chances of Johnson's successor, Hubert Humphrey, who lost to Richard Nixon in 1968.
After that loss, the Democratic Party began to grow more and more troubled. Throughout the 70's and 80's, southern Democrats -- a traditional stronghold of the Democrats -- grew further and further away from the party. Jimmy Carter's election was largely a reaction to Richard Nixon's corrupt administration; after his loss to Ronald Reagan the Democrats' power diminished and there was more and more infighting in the party. However, the election of Bill Clinton in 1992 marked the arrival of so-called New Democrats: a coalition of the most moderate pieces of the old Democratic party. This has led to a new problem for many liberals; to many, the New Democrats are far too close to the post-Republican Revolution, sanitized Republican Party for comfort. This may have contributed to the relative success of Green Party candidate Ralph Nader in the 2000 elections, and the defeat of Democrat Al Gore.