The polls have started closing as one of the tightest US presidential elections in memory draws to a close.
Americans appear to be voting like never before
Final opinion surveys showed Republican President George W Bush and his Democratic challenger John Kerry neck-and-neck.
Tuesday has seen long queues at polling stations amid analysts' predictions of the highest turnout for 40 years.
This could delay the closure of polling stations in the key states of Ohio and Florida, and predictions of the result.
National security and the war in Iraq have dominated the campaign, with the economy largely taking second place.
With the race so close, there are fears of a repeat of the disputed result four years ago and the subsequent legal wrangling.
In crucial swing states like Ohio and Florida, lawyers from the two main political parties have joined international observers to monitor the vote.
There have been complaints of irregularities at polling stations across the swing states, with Republicans and Democrats trading accusations.
EXIT POLLS TO WATCH
0030 GMT: polls close in swing state of Ohio
0100 GMT: Florida, New Hampshire and Pennsylvania
0200 GMT: Minnesota, New Mexico and Wisconsin
0300 GMT: Nevada and Iowa
0600 GMT: last polls close (in Alaska)
However, the BBC's Daniel Griffiths in Washington says election officials nationwide report no major problems at polling stations, though they do say that lines of voters are longer than expected.
ABC News reported that people were having to queue for five or six hours to cast their vote in a polling station at the Driving Park Recreation Centre in a predominantly black suburb of Columbus, Ohio.
The report said voters were sitting in folding chairs and on the gym floor, some of them asking the mayor to call their workplaces in order to explain that they would be delayed.
Pulling up at a polling station in Crawford, Texas, President Bush acknowledged applause before going inside.
"I've given it my all," he told reporters when he re-emerged with his wife Laura. "Who do you trust? I trust the judgment of the American people."
He proceeded to Columbus, Ohio, where he told campaign workers he was confident of victory.
SWING STATE ELECTORAL COLLEGE VOTES
1. Florida - 27 electoral votes
2. Pennsylvania - 21
3. Ohio - 20
4. Minnesota - 10
5. Wisconsin - 10
6. Iowa - 7
7. Nevada - 5
8. New Mexico - 5
9. New Hampshire - 4
Mr Bush later reached the White House where he will watch the returns with his father and former President, George Bush senior.
Mr Kerry started the day in La Crosse in the swing state of Wisconsin, where he addressed supporters, before arriving in Boston where he cast his own vote in the fashionable Beacon Hill district.
"Whatever the outcome tonight, I know one thing that is already an outcome. Our country will be stronger, our country will be united, and we will move forward no matter what," Mr Kerry told reporters.
He was due to watch the results with a small group of family and friends and, at some point, address an open-air rally in a Boston square.
As well as choosing their next president, Americans are also electing a new 435-seat House of Representatives, while voters in 34 states will be choosing new senators.
Just hours before the polls opened in the swing state of Ohio, a federal appeals court cleared the way for political party observers in polling stations to challenge the credentials of voters.
Even a narrow majority would give the winner the state's entire set of 20 Electoral College votes, so every vote matters.
A lower court had barred party observers amid fears that the deployment of Bush supporters in mainly black areas amounted to intimidation.
Though US election officials report no major problems nationwide, some voters in New York and Pennsylvania complained of troubles with non-electronic machines.
America does not have a unified system for casting ballots and such technical difficulties may be inevitable, correspondents say.
Florida, perhaps the biggest swing state of them all, is using electronic voting machines this year to replace the punch cards which created so many problems in the last poll.
The BBC's Susannah Price reports from Miami that memories are still fresh of the weeks of legal wrangling after the elections four years ago, in which George W Bush finally won the state and therefore the election.