So many Sunni Arabs voted that ballots ran out in some places. The strong participation by Sunnis, the backbone of the insurgency, bolstered U.S. hopes that the election could produce a broad-based government capable of ending the daily suicide attacks and other violence that have ravaged the country since the fall of Saddam Hussein.
Difficult times lie ahead, however. The coalition of religious Shiite parties that dominates the current government is expected to win the biggest portion of the 275 seats, but will almost certainly need to compromise with rival factions, with widely differing views, to form a government.
Up to 11 million of the nation's 15 million registered voters took part, election officials estimated, though they had no official turnout figure.
Several explosions rocked Baghdad as the polls opened, including a large one near the heavily fortified Green Zone that slightly injured two civilians and a U.S. Marine, the U.S. military said. An Islamic insurgent group, the Victorious Sect Army, posted a claim of responsibility on a Web site within hours. The claim was not verified.
But violence overall was light and did not appear to discourage Iraqis, some of whom turned out wrapped in their country's flag on a bright, sunny day and afterward displayed a purple ink-stained index finger — a mark to guard against multiple voting.
"The sense I got from speaking to people here in Baghdad was that this is an historic day here and Iraqis are anxious to stand on their own and govern themselves without occupation," reports CBS News correspondent Lara Logan. "Even in hostile Sunni areas that shunned the last election, turnout already appears to be strong."
In other developments:
"There's going to be a real election here and I think there's going to be a significant turnout. That's a very important first step," Biden said on CBS News' The Early Show.
Many Sunnis said they voted to register their opposition to the Shiite-led government and to speed the end of the U.S. military presence.
"Liberation is the most important thing for all Iraqis," said Sunni grocer Omar Badry. "I don't care if we die of thirst and hunger, as long as the Americans leave."
Opposition to the American military presence runs deeper among Sunni Arabs, the minority group which enjoyed a privileged position under Saddam, than among any of Iraq's other religious and ethnic communities.
While Sunnis were defiant, Shiites and Kurds seemed hopeful the new government would be more successful than the outgoing one in restoring security.
A common theme, however, appeared to be a yearning for an end to the turmoil that has engulfed Iraq since the U.S.-led coalition invaded in March 2003 to topple Saddam's regime.
"The first thing we want from the new government is security," said Hussein Ali Abbas, a 66-year-old Shiite as he voted at Baghdad's city hall. "We are surviving but it is a struggle."
It could take at least two weeks before final results are announced, officials said.
Violence was light. Insurgent groups, as promised, generally refrained from attacks on polling stations. In the Sunni Arab militant stronghold of Ramadi, masked gunmen provided by local sheiks guarded polling stations, frisking voters as they entered.
Iraqi leaders expressed relief that the election had passed relatively smoothly.
"The time has come to build Iraq with our own hands and to use the great wealth that God has granted to Iraq to rebuild Iraq so that we can turn our poverty into wealth and our misery into happiness," Prime Minister Ibrahim al-Jaafari said.
The turnout in Anbar province, where the insurgency has been so deadly, was steady all day long, reports CBS News correspondent Cami McCormick. One polling station ran out of ballots at midday. Voters often walked more than a mile in some cases to get to polling places, because civilian cars had been banned from the roads. Some carried Iraqi flags. Some sang and chanted.
In Mosul, Iraq's third-largest city, streets were transformed into a playground, with children playing games and turning roads into soccer fields.
Turnout was most striking in Sunni Arab areas, including the Baghdad district of Azamiyah. Last January, few voters turned out in Azamiyah, where Saddam took refuge when Baghdad fell.
Tareg Moustafa Abdullah, 70, said he regretted boycotting the January election, which allowed Shiites and Kurds to win control. "We ended up with people who do not know God," he said.
In Fallujah, the former Sunni insurgent bastion seized by U.S. forces in November 2004, 11 of the city's 35 polling stations did not receive ballot boxes, while some sites ran out of ballots in the morning, said Mayor Dhari al-Arsan.
He said some voters "thought it was done purposely," but he attributed the lack of ballot boxes to the large turnout. "Today we are witnessing the biggest democratic process," al-Arsan said.
Election commission spokesman Farid Ayar said officials opened only 167 of the planned 207 election centers in Anbar province because of security. Anbar includes Ramadi and Fallujah.
Turnout was also reported high across the Shiite south, including Basra, where the director of one polling center, Amjad Mahdi, estimated more than 70 percent of the 5,000 registered voters at his facility had cast ballots.