Exit polls said Clinton won big among women and older voters, while the young voters who propelled Obama to victory in Iowa did not turn out in big numbers in New Hampshire.
Ann Lewis, a senior adviser to Clinton, said she would be adding staff at all levels as the race moves forward to more states.
Obama won Iowa last week, with Clinton third behind second-place finisher John Edwards, the former North Carolina senator. Edwards finished third in New Hampshire but promised to fight on.
"Two races down, 48 states to go," Edwards said.
In the Republican race, McCain overcame long odds to repeat his New Hampshire win in 2000, when he ultimately lost the nomination to Bush.
McCain, a former prisoner of war in Vietnam, angered the conservative base of his party with his support earlier this year for a now-dead Senate bill that would have given illegal immigrants a path to citizenship.
But after overhauling his campaign staff and recalibrating his strategy, he began to focus on New Hampshire, talking to residents in repeated town hall meetings.
"When the pundits declared us finished I told them I'm going to New Hampshire, where the voters don't let you make the decision for them," McCain said.
Romney, the former governor of neighboring Massachusetts, promised to push on despite pouring tens of millions of dollars of his personal wealth into the presidential race and not managing a breakthrough win.
He finished second to former Arkansas Gov. Mike Huckabee in Iowa's kick-off contest last week. Huckabee, the Baptist minister whose Iowa rise was fueled by his support from religious conservatives, was third in New Hampshire.
Clinton, a New York senator and former first lady, and Romney were both under intense pressure to revive their campaigns after disappointing showings in Iowa.
There were long lines at polling places in New Hampshire amid predictions of a record turnout during the most wide open U.S. presidential race in more than 50 years, with no sitting president or vice president seeking the nominations.
The presidential race now begins to branch out quickly to more states, with Michigan voting next Tuesday, Nevada and South Carolina Republicans on Jan. 19 and South Carolina Democrats on Jan. 26.
South Carolina looms as a potential showdown state in both parties. For Democrats, Obama possibly holds an advantage in a state where more than half of Democratic primary voters are expected to be black.
Michigan is next for Republicans, and McCain, Romney and Huckabee are all looking for wins there. McCain won the state in 2000, Romney grew up there as the son of a former governor and auto executive, and Huckabee will look to make inroads with the state's evangelicals.
