Voting closed at 1300 Jakarta time (0400 GMT, 0600 Prague time) in the archipelago, which spans three different time zones and includes more than 17,000 islands.
Turnout was estimated at between 70 and 80 percent in the capital Jakarta. Indonesia, whose population is 85 percent Muslim, has 153 million eligible voters.
Voters welcomed the opportunity to participate in their country's political future: "I'm happy that we are now able to directly voice our aspirations and directly choose the person we want to lead this country," said one voter.
Many Indonesians see Megawati as ineffectual and aloof.
"I feel more assured because we can vote directly now,” said another. “I don't feel like I am being fooled any more, because now I can directly pick the person I believe should lead this country -- a person who can keep this country secure and who is honest."
Unofficial results will be available tomorrow. But opinion polls suggest the country's incumbent, Megawati Sukarnoputri, will not win enough votes to keep her position.
Megawati, the eldest daughter of Indonesia's founding president, Sukarno, was appointed to the top post in July 2001.
But three years later, Indonesia remains troubled by a weak economy and growing problems with Islamic militants.
Many Indonesians see Megawati as ineffectual and aloof. She made no statement after casting her vote today.
The candidate likely to win the most votes in the election is Susilo Bambang Yudhoyono, an ex-general and Megawati's former security minister. Yudhoyono is relatively new to Indonesian politics. But he has received popularity ratings of more than 40 percent in the past several weeks -- far more than his four other rivals.
He has based his campaign on promises to increase security and battle corruption -- both major points of concern for Indonesian voters.
Yudhoyono is not expected to win 50 percent of today’s vote, which would ensure him a first-round victory. That means he would face the second-place candidate in a run-off in September.
He spoke to journalists in Jakarta after casting his vote: "I am confident I could win in the first round and it means I could go to the second [round]," he said.
Opinion polls show a close battle for the second spot between Megawati, former military chief Wiranto, and moderate Muslim leader Amien Rais. A fifth candidate, incumbent Vice President Hamzah Haz, is expected to win only a small fraction of the votes.
Today’s election is the latest step in Indonesia's sometimes chaotic shift toward democracy.
That shift began in 1998 with the resignation of Suharto, the country's autocratic ruler for 32 years, amid pro-democracy demonstrations.
An amendment to Indonesia's Constitution passed in 2002 mandates that the posts of president and vice president must be directly elected by the people. Before the change, the president had been appointed by Indonesia's upper house of parliament.
There were no major reports of violence or irregularities in Monday's vote. Former U.S. President Jimmy Carter was among the almost 600 international monitors observing the process: "This is a wonderful transition from authoritarian rule to purely democratic rule in just six years, and the people of Indonesia are to be congratulated."
Among today's voters were two of the 33 Muslim militants serving prison sentences for their roles in the 2002 Bali bombings, which killed more than 200 people, mostly Westerners.
The militants, from the group Jemaah Islamiyah, said they staged the attacks to avenge the perceived Western oppression of Muslims worldwide.
None of the five presidential candidates in the vote favors the introduction of an Islamic state. Indonesia is known for its largely moderate practice of Islam and tolerance for other religions.
Final results in the vote are expected in the next two weeks.