The violence on Saturday, which included at least four car bombs in or near Baghdad, occurred despite a security crackdown in the Iraqi capital.
In the deadliest attack, a car bomb struck an Iraqi police checkpoint in al-Maalef district, a Shia area southwest of Baghdad, killing at least 12 people and wounding 38, police said.
Another car bomb targeting the Iraqi army and police killed 11 people.
Fifteen others were wounded when a bomber blew himself up at a joint Iraqi army and police checkpoint in Baghdad's Karrada neighbourhood, an interior ministry official said.
Meanwhile, Aljazeera reported quoting a hospital source in Falluja in western Iraq that eight Iraqis, among them women and children belonging to one family, were killed and six others wounded on Friday night in an air strike by US warplanes.
The bombing targeted a house in Ibrahim Bin Ali district in north-eastern Falluja.
In Saturday's other violent incidents, six people were killed and 25 others were wounded in a roadside bombing in central Baghdad's Haraj market.
Two people died and 14 were wounded when three mortars hit the al-Istarabadi traditional market in Baghdad's Shia neighbourhood of Kadhimiyah.
Another civilian was killed and five wounded in a car bomb attack next to the National Theatre in the Karrada neighbourhood.
In the town of Mahmudiya, 30km south of the capital, a car bomb targeting an Iraqi army checkpoint killed seven people, police said.
The series of attacks took place despite tens of thousands of Iraqi and US troops patrolling the streets of Baghdad since Wednesday as part of a massive security crackdown imposed by Nuri al-Maliki, the prime minister.
Four days into the crackdown, the interior ministry has not yet announced any arrests or other results.
Al-Maliki deployed thousands of
troops on Baghdad's streets
The attacks also come a day after a bomber carrying explosives in his shoes blew himself up in Baghdad's biggest Shia mosque of Baratha, killing 11 and wounding 25 people.
Also on Friday, unknown assailants killed the deputy chief of the municipal council of the small town of Daghara and his two sons, police said. The killing of Rasim Moussa took place near his house at night.
In another incident, a civilian was killed in a drive-by shooting near his house in the town of Mahaweel, 75km south of Baghdad, police said.
US soldiers missing
Meanwhile, US military helicopters and divers searched for two US soldiers missing after an attack on Friday in which one American soldier was killed in Yusufiya in the "Triangle of Death" south of Baghdad.
Major-General William Caldwell, the spokesman for the US military in Iraq, said "we are using all available assets, coalition and Iraqi - ground, air and water - to locate and determine the duty status of our soldiers".
He said teams of divers were searching the canals and Euphrates river near Yusufiya, a rural area which has seen fierce fighting between US forces and fighters.
More than 2,500 US soldiers have died in Iraq since the US-led invasion in 2003.