Obama has retained a lead in most nationwide opinion polls and has the advantage in most of the battleground states, which are expected to decide the election.
Election 'upset' vow
But John McCain, his Republican rival, has dismissed the opinion polls and promised an upset.
Obama cast his ballot at a school gymnasium in his home city of Chicago with his wife and daughter by his side, while McCain voted in his home state of Arizona.
In a highly unusual move, both McCain and Obama got back on the campaign trail on election day itself, before planning to head to their respective home bases to watch the results come in.
"He is going to travel to Colorado and New Mexico, and appears to be breaking with the usual tradition of ending one's campaign on election day," said Al Jazeera's Tom Ackerman, reporting from Phoenix, Arizona.
In Indiana, Obama met campaign workers and made several phone calls to undecided voters, warning the race was going to be tight.
"The question is; 'who wants it more?'" he told about 30 union activists gathered in a campaign office.
Joe Biden, Obama's running-mate, cast his ballot alongside his 91-year-old mother and wife, Jill, in his hometown of Wilmington, Delaware.
Sarah Palin, the Republican vice-presidential candidate, voted in the small town of Wasilla, Alaska, where she began her political career as mayor.
Voting problems have surfaced in several areas in the eastern United States.
In some New Jersey precincts, voters had to use paper ballots because of problems with electronic voting machines.
In Virginia, lawsuits alleging voter suppression have been filed.
A day earlier, a judge refused to extend polling hours or provide extra voting machines to predominantly African-American suburbs, after the National Association for the Advancement of Coloured People (NAACP) had demanded the changes in a federal lawsuit.
The NAACP had argued that minority areas would experience overwhelming turnout and there were not enough electronic machines to cater for all voters.
Voter registration numbers are up 7.3 per cent from the last presidential election.
Al Jazeera's Sarah Brown, reporting from Chicago, said: "There are some incredible scenes with lines of voters queueing around the block at some polling stations.
"At some places people started lining up at 5am and had to wait up to two hours to vote. As expected, Obama's hometown is doing him proud - of more than 30 voters polled informally all but one were for the Democratic candidate."
Al Jazeera's Sebastian Walker, reporting from Florida, also said voter turnout there was high.
"The main reason that many people came early to vote is they were afraid their votes may not be recorded if they were to cast their ballots later in the day," he said.
"This is an important state, and people are aware of how tight it will be.
"The elderly here have a close alignment with the Republican party and John McCain and, while he is trailing in numerous polls here, Florida is a vital state," he said.
"It is also a state where voting irregularities have been witnessed, and that is still fresh in the minds of many people here."
Residents of Dixville Notch and Hart's Location, two villages in New Hampshire with just 115 residents between them, were the first to cast their votes on election day, going to the polls at midnight local time (0500 GMT Tuesday).
Obama won by 15 votes to six in Dixville Notch, which has opened its polling station shortly after midnight at every election since 1960.
The Democratic candidate won by 17 votes to 10 in Hart's Location.
George Bush, the outgoing president, won the votes in Dixville Notch and Hart's Location on his way to re-election in 2004.
The first polls begin to close in parts of Indiana and Kentucky at 6pm local time (2300 GMT). Voting ends over the next six hours in the other 48 states.
On the final full day of campaigning, McCain, the Arizona senator, launched a major tour of seven states including Florida, Virginia, Pennsylvania, Tennessee, Indiana, New Mexico and Nevada before heading to his home state.
|The Obamas voted early in Chicago
Obama told supporters on Monday they were "one day from change" as he travelled through North Carolina, Florida and Virginia.
But the event was overshadowed by the death from cancer of his maternal grandmother, Madelyn Dunham, at the age of 86.
He had suspended his campaign last week for two days to visit a hospital in his native Hawaii to be at the side of the woman who acted in many ways as his surrogate mother.
Under the US political system, the president is elected not by direct popular vote but by capturing 270 out of 538 electoral votes distributed throughout the country in a state-by-state contest.
Obama leads McCain in five of eight key battleground states, according to a series of Reuters/Zogby polls released on Tuesday.