UN officials and foreign observers said that turnout was high and voting was mostly orderly and peaceful at the landmark polls.
"We believe the enthusiasm being shown at this election shows the willingness of the population to move ahead, to move out of 40 years of misrule and misery," said Ross Mountain, the UN deputy special representative for the Congo.
"To imagine a successful, stable Africa with an unstable Congo is a little hard to do," he said.
After polls closed on Sunday, officials counted ballots by lamplight into the night at some 50,000 voting stations across Democratic Republic of Congo.
Official results from the war-ravaged nation the size of western Europe are due within three weeks.
President Joseph Kabila is regarded as favourite to win a five-year term. His main rivals, former rebel chiefs Jean-Pierre Bemba and Azarias Ruberwa, have criticised "irregularities" in voting, raising the prospect they may question the result.
Youths destroyed several polling stations in the southern West and East Kasai provinces, an opposition stronghold, after voting was over.
In the southeast town of Lubumbashi, students protested when they found they were not registered to vote, but these appeared to be isolated incidents.
"I have witnessed long queues and busy polling stations," European member of parliament Richard Howitt, one of more than 1,200 international observers, told Reuters from Lubumbashi.
Turnout was heavy in the violence-plagued east, a stronghold of 35-year-old Kabila. Initial counts from some individual polling stations there showed a strong lead for the president, who took office when his father Laurent was killed in 2001.
Standing against Kabila were 31 challengers, including several former rebel leaders who fought in the five-year war that devastated the central African country already crippled by 32 years of misrule under dictator Mobutu Sese Seko.
If no candidate wins more than 50 percent of Sunday's vote a run-off between the two leading candidates will be held on October 29, the national electoral commission said.
More than 9,700 other candidates were bidding for 500 parliament seats in the polls.
Securing the vote
Many of the more than 25 million registered voters got up early to cast their ballots. Others waited patiently in line for hours.
Protected by the biggest peacekeeping operation in the world the elections held in the former Belgium colony were the most complex and expensive ever organised by the UN, at a cost of $460 million.
UN peacekeepers, 17,000 of them, backed by 1,100 EU troops and Congolese police guarded the schools, churches and tents used as polling stations.
Congo has one third of the world's cobalt reserves, as well as copper, gold and diamonds. However, it has known little but war and dictatorship since independence in 1960.
"This is a great event. I'm 44 years old and this is the first time I've ever voted," said Zawadi Unega in Kinshasa.