Heading into Election Day, Clinton held a narrow advantage, leading Trump by 4 points in the last NBC/Wall Street Journal poll taken before Tuesday.
In a parallel storyline, Democrats and Republicans are battling for control of the Senate.
In an interview with ABC's "Good Morning America", Democratic vice-presidential nominee Tim Kaine said Clinton can clinch victory if she wins any of the "checkmate" battleground states, especially North Carolina, Pennsylvania, Florida and OH in that category.
The campaign focused on the character of the candidates: Clinton, 69, a former USA secretary of state, and Trump, 70, a NY businessman. But his path to the 270 electoral votes needed to capture the White House appears to be narrow. Republicans are widely expected to keep control of the House of Representatives.
Clinton and her husband, former President Bill Clinton, voted at their local polling station in Chappaqua, New York, just after 8 a.m. ET.
Polls in the Eastern time zones of in and Kentucky were the first to close, and a flood of vital battleground states such as Virginia, North Carolina and OH - where polls were due to close in the next 90 minutes - would provide initial clues of the possible victor.
Clinton never mentioned the Federal Bureau of Investigation review Monday and appeared already to be preparing for the challenges awaiting her after Tuesday.
Some good news boosted Mrs Clinton's spirits in the final moments of the campaign.
"We know enough about my opponent, we know who he is", Clinton said as she addressed the 33,000-person crowd, her largest of the campaign. "The real question for us is what kind of country we want to be". As he surveyed a crowd in Scranton, Pennsylvania, he declared: "It's been a long journey".
Trump again raised the possibility on Tuesday of not accepting the election's outcome, saying he had seen reports of voting irregularities.
Financial markets, betting exchanges and online trading platforms largely predicted a Clinton win, although Trump's team said he could pull off a surprise victory like the June "Brexit" vote to pull Britain out of the European Union.
"We have to win", Trump said at his final campaign event in Grand Rapids, Michigan, on Monday night. "Do not let this opportunity slip away". Trump called into Fox News on Election Day and was asked if he would concede the election if he loses.
The poll of more than 10,000 people who voted in the election showed a majority anxious about their ability to get ahead, with little confidence in political parties or the media to improve their situation. About half of those votes were cast under the shadow of the Federal Bureau of Investigation director's initial announcement of a new email review.
In Florida alone, Hispanic participation was up by more than 453,000 votes, almost doubling the 2012 level. That's about 18 per cent of the expected total votes for president.