No one has claimed responsibility for the attacks.
Violence in Iraq has eased since its height in 2006-2007 when sectarian fighting killed thousands of people, but Sunni Islamists and an al Qaeda affiliate still launch regular attacks, seeking to undermine the Shi`ite-led government.
The most deadly explosion took place in Taji, 20 km (12 miles) north of the capital Baghdad, where bombs in three parked cars went off separately, killing eight people and wounding 22.
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.
In Baghdad, a parked car bomb killed two people in a northwestern district. Another blast near a public market in Khan Bani Saad, 30 km (20 miles) northeast of the capital, killed one civilian and wounded several policemen.
Two more policemen were killed when a car bomb went off in the town of Balad Ruz, 90 km (55 miles) northeast of Baghdad.