The latest projected results have Obama, a Democrat, winning 275 electoral votes and Romney with 203 Electoral College votes.
The projections say Obama has won in the District of Columbia and 20 states, including the battleground states of Ohio, Iowa, New Hampshire and Pennsylvania. Romney has won in 23 states including the battleground state of North Carolina and the state of Indiana, which went for Obama last election. The battleground states of Florida and Virginia are too close to call.
The candidates made a final push for support Tuesday as voters waited in long lines at polling places. Some sporadic problems were reported, and both candidates dispatched lawyers to monitor the voting for any irregularities.
Polls remained open to allow people still in line at closing time to cast ballots.
The Justice Department has nearly 800 observers in 23 states to respond to any allegations of fraud.
After a year-and-a-half of campaigning, three debates and thousands of televised campaign ads, nationwide pre-election surveys showed the two candidates in a virtual deadlock.
But the surveys also showed Obama with a slight edge in a handful of those key battleground states that are likely to determine the outcome.
U.S. presidential elections are not decided by the national popular vote, but rather by the Electoral College system, developed more than 200 years ago, in which each of the 50 states' influence on the outcome is roughly equivalent to its population.
A candidate needs at least 270 of the available 538 electoral votes to win the election.
Voters also are electing all 435 members of the House of Representatives, and 33 of the 100 members of the Senate. Analysts generally say Republicans will continue to hold their majority in the House, while the president's Democratic Party could maintain its slim majority in the Senate.
Millions of Americans cast ballots in early voting, in the last month.
Obama voted a few days ago in his home city of Chicago, and spent Tuesday there. He conducted interviews for broadcast in key states and played basketball with friends, one of his Election Day traditions. He also called voters from a campaign office.
Romney, a one-time venture capitalist, voted Tuesday morning in Massachusetts, the northeastern state he once governed but where Obama won. He also made a final push for votes in the key states of Ohio and Pennsylvania.