At least 57 killed in co-ordinated Baghdad attacks
The interior ministry said 13 locations had been attacked, including al-Amil in the south of the city and Halawi and Karrada closer to the centre.
The bombings are the worst in months - and follow the withdrawal of US troops.
They come amid fears of rising sectarian tensions as the unity government faces internal divisions.
It was not immediately clear who was behind the attacks.
However, analysts say the level of co-ordination suggests a planning capability only available to al-Qaeda in Iraq.
Bombings remain common in Iraq despite an overall fall in violence.
In al-Amil there were two blasts, the second of which appeared to target rescuers who had come to the scene of the first explosion.
Raghad Khalid, a teacher at a kindergarten in Karrada, said all their windows had been blown out.
"The children were scared and crying. Some parts of the car bomb are inside our building."
Smoke was seen rising over Karrada district, with ambulances rushing to the scene.
Another woman said her baby had been covered in glass.
"She is now scared in the next room. All countries are stable. Why don't we have security and stability?" said Um Hanin.
Political turmoil
Iraq's year-old power-sharing government is in turmoil after an arrest warrant was issued for Sunni Vice-President Tariq al-Hashemi on terror charges.
The entire al-Iraqiyya group, the main Sunni bloc in parliament, is boycotting the assembly in protest. It accuses Iraqi Prime Minister Nouri Maliki, a Shia, of monopolising power.
Mr Hashemi denies the charges. He is currently in Irbil in Iraqi Kurdistan, under the protection of the regional government, but Mr Maliki has demanded that they give him up.
The last American troops departed from Iraq on Sunday, nearly nine years after the war that toppled Saddam Hussein in 2003.
President Barack Obama acknowledged that the situation was not perfect, but said the US forces were leaving behind "a sovereign, stable and self-reliant Iraq, with a representative government elected by its people".