The United States condemned the attacks, offering Iraqi forces assistance in bringing those responsible "to justice." United Nations envoy to Iraq Martin Kobler also condemned the violence.
Baghdad was hit by 10 bomb attacks and two shootings that killed at least 28 people and wounded dozens more, according to an interior ministry official and a medic.
The deadliest attack in the capital saw a car bomb explode in the Karrada neighbourhood of central Baghdad where pilgrims were eating breakfast in tents.
Human remains were scattered across the street, while cars and shops in the area were damaged, an AFP journalist said.
The attack, in which a medical official said 16 people died and 32 were wounded, appeared aimed at the Shiite pilgrims as they headed in their tens of thousands to Imam Kadhim shrine in the northern neighbourhood of Kadhimiyah.
Another car bomb on the outskirts of Kadhimiyah, which an interior ministry official and the medic said killed seven people, left a hole two metres (yards) deep in a street, damaged cars and destroyed a number of makeshift houses.
"I could not see for more than two metres because of the smoke and dust," said a resident, Abdul Zahra Abdul Saad, adding that the blast occurred at about 5:00 am (0200 GMT).
"It took out three people: two children and an old woman. They were all dead."
Coordinated attacks took place across other centres, including in the central city of Hilla, where a police captain and doctor Ali al-Khafaji said two car bombs killed 20 people and wounded 51 others.
Ten people, meanwhile, were killed in a wave of attacks in and around Baquba, north of Baghdad, security and medical officials said.
In the northern city of Kirkuk, three car bombs killed two people and wounded at least 17 more, the interior ministry official and doctor Nabil Hamdi Mushnaq of Kirkuk hospital said.
Marwan Ibrahim, a 34-year-old journalist who has worked for AFP since 2003, was wounded by a car bomb while reporting on the attacks in Kirkuk.
In other incidents, five people were killed and 30 wounded in two car bombs in Balad, north of Baghdad, including one which targeted the local headquarters of the Shiite endowment.
Car bombs in Al-Azizyah, south of Baghdad, and in the restive northern city of Mosul killed a total of four people, while 24 people were wounded in a blast near the holy city of Karbala in central Iraq.
And west of Baghdad, insurgents killed two policemen in an attack on a checkpoint near Fallujah, while a magnetic "sticky bomb" killed a health directorate employee in Heet, police Lieutenant Colonel Haidar al-Jaafari said.
Along with the security forces, the Shiite majority in Iraq has been a main target of Sunni Arab armed groups since the US-led invasion of 2003 toppled now executed dictator Saddam Hussein's Sunni-dominated regime.
Wednesday's attacks come during a political row that has seen opponents of Prime Minister Nuri al-Maliki mounting an attempt to oust him, but so far failing due to a lack of votes.
Maliki's opponents have for months accused him of monopolising decision-making and moving toward dictatorship.
A statement on Maliki's website on Wednesday said that he had warned during a meeting against "political differences that ... may negatively affect the security situation."
The Iraqiya bloc, one of the parties pushing for Maliki to be unseated, said that it "holds the government and he (Maliki) who controls ... the security forces fully responsible for establishing security."
Violence across Iraq has declined dramatically since the 2006-2007 peak but attacks remain common, especially in Baghdad. A total of 132 Iraqis were killed in May, official figures show.