President Bush told a gathering of Iraqi-Americans last week that everyone in the new Iraq will enjoy freedom, "whether you're Sunni or Shia or Kurd or Chaldean or Assyrian or Turkoman or Christian or Jew or Muslim, no matter what your faith."
Given that complex makeup, however, creating effective government is a daunting challenge.
Few places on earth draw upon a richer religious heritage, and a sense of this mosaic underscores the enormity of America's task.
In the Bible, Iraq was the homeland of Abraham, the forefather of Jews, Christians and Muslims, and it is the country where rabbis compiled the Babylonian Talmud that defines traditional Judaism though few Jews remain.
Islam's golden age under the Abbasid caliphs was centered in Baghdad from the eighth to 13th centuries, and Iraq is the holy land of major shrines for Muslim Shiites.
The division between the Shiites and rival Sunnis is fundamental both to Islam, and to Iraq's current political situation.
The split originated when Islam's founding Prophet Muhammad died and Sunnis said he wanted his successors chosen by consensus. Shiites argued the prophet intended leaders to come only from his family line.
Today, Sunnism claims 85 percent of the world's 1.2 billion Muslims. Iraq, however, has a Shiite majority (often put at 60 percent, though there are no standard statistics).
But Iraq's Shiites are not a single bloc. Most are Arabs, including culturally separate "marsh Arabs," and there are some Shiites among nomadic Bedouins. Other Shiites can be found among ethnic Kurds, and among the Turkomen who make up perhaps 5 percent of all Iraqis.
Iraq's Sunni minority, meanwhile, is divided into two major groups, the Kurds and Arabs. The Arab Sunnis dominated in Saddam Hussein's regime and repressed both Kurds and Shiites.
The Kurds (estimated at 15 percent to 23 percent of all Iraqis) are divided among themselves by politics, tribe and dialect, yet united by ethnic pride and desire for regional autonomy or their own state.
For the Kurds, "ethnicity matters more than their religion," says Shiite political scientist Vali Nasr of California's Naval Postgraduate School.
Christians in Iraq represent only about 3 percent of the population, but they are well-educated and wielded some influence under Saddam. They belong largely to Iraq's distinctive Chaldean Catholic and Assyrian churches, and are calling for protection of minority rights under the new regime.
Iraq's smaller minority religions include the unique Mandeans, who regard Jesus as an apostate and revere John the Baptist. There also are Yazidis, who believe the devil rules the world.
But ultimately Iraq is a Muslim nation.
And when Saddam's regime fell, Iraq "went from a Sunni to Shiite country overnight," Nasr says.
That fact was dramatized in pilgrimages to the Shiite holy cities of Najaf and Karbala over the past two weeks, with more than 1 million worshippers in the streets.
Given that groundswell and simple math, it seems that if the United States sets up elections in Iraq, Shiite candidates will likely dominate in many places. Nasr doubts that even secularized or mildly religious Shiites would vote for Sunnis.
And Shiite religious leaders will want a major say in the educational system, says Shama Inati, a professor at Villanova University.
Abdulazia Sachedina of the University of Virginia, who trained in both Shiite and Sunni schools, says the Shiite religious system enhances the importance of clerics.
"Sunni religious leaders don't have power or credibility with the people. They're government appointees," he says. By contrast, the Shiite leaders, called ayatollahs, are supported by people who freely choose to give them donations. Says Sachedina: "The layman is really connected closely with the ayatollah."
What sort of regime might Shiism produce?
Scholars think a truly representative regime would have some sort of Islamic cast: It wouldn't be a secular democracy with American-style separation of church and state.
The majority of Iraqis, and 90 percent or more in neighboring Iran, follow Shiism's Ithna Ashari ("Twelver") branch, so some wonder whether Iraq will imitate Iran's 1979 revolution and install rule by clerics.
Despite the clerics' importance, Nasr and Sachedina say no.
Iraq and Iran have different languages and cultures, for one thing. More importantly, clerical rule actually violates Shiite tradition so the Iranian revolution was a break from the past. Teachers like Ayatollah Ali Hussein al-Sistani, generally considered Iraq's highest religious authority, have opposed Iran's theocratic system.
Still, though the ayatollahs now maneuvering in Iraq will not hold political office, Sachedina predicts, their devoted followers something like 40 percent of the Shiite population will obey their endorsements of candidates and fatwas (religious edicts) they issue on political policy.
As for the Sunnis, they are now organizing through mosques, Nasr says. Uniting as a political force was something they didn't need to be concerned about while Saddam was in power.
Sachedina is worried about inroads being made among Sunnis by Saudi Arabia's puritanical Wahhabi movement, which has been connected with the rise of extremism and despises Shiism.
But Inati, an Orthodox Christian from Lebanon, believes that Iraq's complex and pluralistic nature will help the country in the end.
Iraq is so diverse that even those calling for an Islamist state "will try to be tolerant because they know it will not work out otherwise."
She also is optimistic about postwar relations between Islam's two main branches. Shiites, she says, "felt poorly treated the last 30 years not by the Sunni population" but by Saddam.