More than 18 million Romanians are eligible to vote, but none of the dozen candidates is expected to get more than 50 percent of the vote in the first round. That means a runoff election is likely on Dec. 6.
Polls opened at 7 a.m. (0500 GMT) and will close at 9 p.m. (1900 GMT).
Romania slipped into political crisis when Parliament dismissed the two-party government of Emil Boc on Oct. 13 after a dispute between the coalition partners over control of the Interior Ministry, which oversees the presidential vote.
The Social Democrats said the Liberal Democrats, who are close to Basescu, wanted to run the ministry so they could control the presidential vote and allow election fraud.
Parliament then failed to vote on another government, and Boc has run a caretaker government with limited powers since October.
Romania's economy, already in a deep recession, is expected to shrink some 8.5 percent this year. The International Monetary Fund blocked a euro1.5 billion (US$2.22 billion) loan because Romania does not have a government or 2010 budget.
Romania needs the loan to pay state sector salaries and pensions, but is unlikely to get it before the new year. Some 1.3 million state workers will be forced to take eight days of unpaid leave by the end of 2009.
Basescu, 58, styles himself as a patriot with a deep respect for Romanian traditions and awareness of the concerns of average voters.
The former ship captain has seen his popularity drop this year due to the economic downturn and political feuding, but still enjoys wide support, especially in rural areas.
He takes credit for raising Romania's international profile by leading into the European Union on Jan. 1, 2007, and hosting a major NATO summit in 2008 - the high point of his presidency.
However, he is blamed by his critics for stirring political unrest and associating with allegedly corrupt business people.
The president has a stormy relationship with Parliament which impeached him in 2005. He survived as president after Romanians voted not to remove him from office in a referendum.
To coincide with Sunday's vote, Basescu has organized a referendum to reduce the number of lawmakers and remove one parliamentary chamber, a move many see as retaliation for his impeachment.
Geoana, 51, who served as Romania's ambassador to the U.S. and then as foreign minister, lacks Basescu's popular appeal but is seen as a clever negotiator in Romanian politics. His Social Democratic Party, the successor to the Communist Party that ruled Romania for more than 40 years, has a strong grass-roots organization in both rural areas and cities.
Recent opinion polls have given Basescu about one-third of the vote, a slight edge over Geoana. A third candidate, who has made strides in recent weeks, is Liberal Party leader Crin Antonescu, a skillful debater.
More than 1,000 Romanian and foreign observers will monitor the elections amid concerns that voter fraud would be hard to detect because the presidential ballot and the referendum are taking place at the same time.