Early vote-counting in Ohio, Virginia and Florida showed a deadlocked picture with Obama and Romney running neck-and-neck. Romney needs all three to navigate a narrow path to the presidency, while Obama can afford to lose one or two of them and still win a second term.
At least 120 million people were expected to render their judgment between the Democratic incumbent and Romney after a long and bitter presidential campaign that magnified the differences between Americans wanting to continue Obama's approach to fixing the ailing economy and those who want to try a new path.
CNN said exit poll data showed a deadlock in Virginia, with each man gaining 49 percent.
Television networks projected Romney the winner, as expected, in Republican states Kentucky, West Virginia, Oklahoma, South Carolina and Indiana.
Obama was projected the winner in the Democratic strongholds of Maryland, Vermont, Connecticut, Delaware, Washington D.C., Massachusetts and his home state of Illinois.
CNN projected Obama carried Maine.
Who Americans choose will set the country's course for the next four years on spending, taxes, healthcare, the role of government, and foreign policy challenges such the rise of China and Iran's nuclear ambitions.
Each man offered different policies to cure what ails America's weak economy, with Obama pledging to raise taxes on the wealthy and Romney offering across-the-board tax cuts as a way to reignite strong economic growth.
National opinion polls before the vote show Obama and Romney in a virtual dead heat, although the Democratic incumbent has a slight advantage in several vital swing states - most notably Ohio - that could give him the 270 electoral votes needed to win the state-by-state contest.
According to Reuters-Ipsos Election Day polling, one in three Obama voters said the economy was the most important issue for them, while half of Romney voters agreed. Healthcare was the second most important issue for Obama voters and the budget deficit was second for Romney voters. Unemployment was third for both.
Three-quarters of both Romney and Obama supporters decided to vote for their preferred candidate before the October debates, according to the data.
The Romney side was encouraged by what was described as heavy turnout in Republican areas from Florida to Colorado.
Romney made last-minute visits to Ohio and Pennsylvania on Tuesday to try to drive up turnout in those states, while Vice President Joe Biden was dispatched to Ohio. Obama remained in his hometown of Chicago.
Expressing confidence, Romney told reporters on his plane as he flew back to Boston that he had written only one speech for evening, one celebrating his victory.
"I'm very proud of the campaign that I've run, to tell you the truth," he said. "I'm sure like any campaign, people can talk to mistakes, but that's going to be part of anything that's produced by human beings," he said.
Obama told a Denver television station he had speeches ready for either outcome. "You always have two speeches prepared because you can't take anything for granted," he told FOX31.
The multimillionaire former head of a private equity firm and a former governor of Massachusetts, Romney would be the first Mormon president and one of the wealthiest Americans to assume the nation's highest office.
Obama, the country's first black president, seeks to avoid being relegated to a single term, something that has happened to only one of the previous four occupants of the White House.
Whichever candidate wins, a razor-thin margin might not bode well for the clear mandate needed to help break the partisan gridlock in Washington.
Fuelled by record spending on negative ads, the battle between the two men was focused primarily on the lagging economic recovery and persistently high unemployment, but at times it turned personal.
The close race raises the prospect of a disputed outcome similar to the 2000 election, which ended with a U.S. Supreme Court decision favouring George W. Bush over Al Gore after legal challenges to the tight vote in Florida. Both the Romney and Obama campaigns have assembled legal teams to deal with possible voting problems, challenges or recounts.
COMPLAINTS AND FRUSTRATION
Although voting appeared to go smoothly in most places, complaints about procedures and possible irregularities surfaced sporadically across the electoral map. But there were no immediate claims of anything widespread or systematic enough to cast doubt on the credibility of the election outcome.
Storm-weary residents across New York and New Jersey encountered long lines as they went to cast their ballots just over a week after the devastating storm Sandy caused havoc in the region. New Jersey granted a last-minute extension to the deadline for email voting.
The balance of power in the U.S. Congress will also be at stake in races for the Senate and House of Representatives that could affect the outcome of "fiscal-cliff" negotiations on spending cuts and tax increases, which kick in at the end of the year unless a deal is reached.
Obama's Democrats are now expected to narrowly hold their Senate majority, while Romney's Republicans are favoured to retain House control.
(Additional reporting by Jeff Mason in Chicago, Patricia Zengerle in Boston, Edith Honan in New York, Brendan O'Brien in Milwaukee, Dave Warner in Philadelphia, Philip Barbara in New Jersey, Matt Spetalnick, Lisa Lambert, Susan Heavey, Thomas Ferraro, Susan Cornwell, Anna Yukhananov and Roberta Rampton in Washington; Writing by Steve Holland and John Whitesides; Editing by Claudia Parsons, Christopher Wilson and Jim Loney)