Most of the attacks early on Saturday appeared to have targeted security forces, including a large car bomb in Zayuna that went off as a US patrol passed but killed only two Iraqi bystanders, Brigadier Abdul Karim Khalaf, an interior ministry spokesman, said.
In the central Baghdad neighbourhood of Waziriyah, a man attempted to ram his car into a police station and was shot, but not before he detonated the explosives in the vehicle, killing a policeman and wounding 10 other people.
Smaller blasts in other parts of the capital wounded another half-dozen civilians, Khalaf added.
Gunmen opened fire on two employees of the state-owned Sabah newspaper as they drove to work, killing one and wounding the other, a security official said.
In the northern oil city of Kirkuk, twin blasts killed four people and wounded 16.
The bombers detonated the second device as a police patrol arrived on the scene of the first blast, killing one officer and wounding two, said Lieutenant Colonel Akram Abdullah of Kirkuk police.
South of Baghdad, authorities discovered the bodies of five people who had been shot dead, four of them in the town of Suwayrah, which has become a common dumping ground for victims of sectarian killings.