The violence comes a day after a wave of attacks against members of the security forces left nine police officers and soldiers dead and 11 wounded.
In the deadliest attack, two roadside bombs exploded in an area about 40 kilometres north of Hilla, which lies south of Baghdad.
The bombings killed police Lieutenant Colonel Salman Kadhim al-Khazraji, two other policemen and a civilian and wounded two other police, an officer in the Babil police media office and a doctor from Hilla hospital said.
Gunmen also shot dead two soldiers and wounded a third at a checkpoint near Iskandiriyah, 50 kilometres south of Baghdad, an army first lieutenant and a medical source said.
A policeman was killed and another wounded by a roadside bomb that targeted a checkpoint in a village near Balad, north of the capital.
Gunmen also killed a civilian in the north Iraq city of Mosul, police and a doctor there said.
While insurgents opposed to the Baghdad government are regarded as weaker than in past years, they have shown they can strike at even the most highly secure sites.
Targets in recent months have included a police station, a military base, the anti-terrorism directorate in Baghdad, a prison and an entrance to Baghdad's heavily fortified Green Zone, where the Iraqi government is headquartered.