In Taji, 20 km (12 miles) north of Baghdad, bombs in three parked cars went off separately, killing 11 people and wounding 24, including several policemen, Reuters reported. Taji has one of Iraq's largest military airbases but the bombing hit a civilian neighborhood.
In Baghdad, a suicide car bomb and two parked car bombs went off, killing eight people, including a police officer, and wounding another 11.
Civilians were among those killed and injured in the attacks around the capital, but the aim of the attackers seems to have been to kill as many security personnel as possible, the BBC reported.
Another blast targeted a bus carrying Iranian pilgrims as it passed through the town of Madaen, about 30 km (20 miles) southeast of Baghdad, killing two passers-by and wounding another ten, including seven Iranians.
A suicide bomber in a car blew himself up in the city of Kut, 150 km (95 miles) southeast of Baghdad, killing four policemen, police and local officials said.
Two more policemen were killed when a car bomb went off in the town of Balad Ruz, 90 km (55 miles) northeast of Baghdad.
In Mosul, 390 km (240 miles) north of Baghdad, a parked car bomb and two roadside bombs blew up separately, killing a civilian and wounding six.
No group claimed responsibility for the wave of attacks, but a local al Qaeda affiliate and other Sunni Islamist groups have carried out at least one major assault a month since the last American troops left in December.
A resident of the Ammil district in Baghdad accused fugitive Vice-President Tariq al-Hashemi and pro-Sunni media organisations of inflaming passions against Iraq's Shia majority.
"They are the terrorists," he told Reuters news agency. "They want to terminate the Shia. They want to see all the Shia gone."
Hashemi was recently sentenced to death in absentia after an Iraqi court found him guilty of running death squads.