Barack Obama and Mitt Romney have spent the day before the election visiting key swing states and making final pitches to voters.
Mitt Romney went to Florida, where polls suggest he has the edge, and then to Virginia, New Hampshire and Ohio.
President Barack Obama appeared in Iowa, Wisconsin and Ohio, joined at rallies by Bruce Springsteen and rapper Jay-Z.
The election will be decided in just a handful of states, with Ohio in particular seen as crucial to victory.
Barack Obama closed his re-election campaign in Des Moines, Iowa, – the city where his bid for the presidency began in early 2007.
At a late-night rally, he told the crowd that Iowa had started “a movement that spread across the country”.
Mitt Romney, meanwhile, was due to end his campaign with a late-night rally in New Hampshire but made the surprise announcement that he would extend campaigning into election day itself – visiting Ohio and Pennsylvania on Tuesday.
Barack Obama and Mitt Romney are running almost neck-and-neck in national polls, in a campaign that has cost more than $2 billion.
But surveys of the nine or so battleground states that will determine the election show Barack Obama narrowly ahead.
On the stroke of midnight, the first votes were cast and quickly counted in the tiny village of Dixville Notch in New Hampshire. They resulted in a tie with five votes each for Barack Obama and Mitt Romney.
The race has been most intense in Ohio – no Republican has ever made it to the White House without winning there.
Mitt Romney would become the first Mormon president of the US if he wins on Tuesday.
In Fairfax, Virginia just outside Washington DC, the former Massachusetts governor said the president had failed to make good on the promise of his 2008 campaign and it was time for a new direction.
“Look at the record,” he exhorted supporters.
“Talk is cheap, but a record is real and it’s earned with effort. When the president promised change, you can look and see what happened. Four years ago then-candidate Obama promised to do so very much but he’s done so very little.”
He summed up his pitch to voters: “Do you want four more years like the last four years? Or do you want real change?”
In Ohio, Bruce Springsteen and rapper Jay-Z helped warm up a crowd for Barack Obama before the president appeared.
“I’ve got a lot of fight left in me and I hope you do,” Barack Obama told the rally, his voice hoarse from nearly non-stop campaigning.
“The folks at the very top in Washington don’t need another champion. They’ll always have a seat at the table. The people who need a champion are the people whose letters I read every day.
“We’ve come too far to turn back now. We’ve come too far to let our hearts grow faint.”
Thirty million Americans have already cast their ballot through early voting across 34 states. In the 2008 presidential election, 130 million people voted.
With the election expected to be decided by a razor-thin margin, both sides are readying teams of lawyers for legal fights.
Democrats in Florida have filed a legal case demanding an extension of time available for early voting, citing unprecedented demand after voters reportedly queued up for hours on Sunday,
In Ohio, Republican election officials were going to court on Monday to defend an 11th-hour directive to local election officials that tightens requirements needed for provisional ballots to be counted.
In New York, Governor Andrew Cuomo has signed an order allowing residents to vote at any polling place, not just the one to which they had been assigned.
The city and surrounding areas were devastated by super-storm Sandy last week. Many residents remain without power and many polling places were damaged.
Activists have been stepping up efforts across the crucial swing states.
In Wisconsin, student volunteers have been putting in 14-hour days in an effort to deliver the state for Barack Obama.
Average of national opinion polls shows Barack Obama heading into election day with a single-point lead among likely voters, 49% to 48%.
Mitt Romney remains favored among whites, older people and evangelical Christians; Barack Obama among women, non-whites and young adults.
In the crucial swing state of Ohio, a RealClearPolitics.com average of polls shows Barack Obama leading Mitt Romney 49.6% to 46.6%.
The election is decided by the electoral college. Each state is given a number of electoral votes in rough proportion to its population. The candidate who wins 270 electoral votes becomes president.
A handful of governors, the entire House of Representatives and one-third of the Senate are also up for election on Tuesday.
Republicans are expected to keep control of the House, while Democrats were tipped to do the same in the Senate.