The deadliest attack was in Kazimiyah district in northern Baghdad, where militants in a speeding car went on shooting spree that killed three civilians and wounded another, two police officers said.
The violence was the latest to his the country in what has been a particularly bloody month. Some 300 people have been killed in attacks over the past two weeks.
In the northern city of Mosul, a car bomb went off at a house early in the morning while a joint army-police unit was conducting door-to-door searches.
Twenty people, including four civilians, were wounded.
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Also in Mosul, police said militants gunned down a policeman in his car in the city center.
Authorities also found a body floating in the Tigris river, shot at close range with hands bound behind the back. Mosul, some 360 kilometers northwest of Baghdad, is a former stronghold of Sunni militants.
In Iraq's western province of Anbar, the birthplace of the Sunni insurgency led by al-Qaida in Iraq, three soldiers were killed and five wounded in two separate attacks by roadside bombs on their patrols, police and army officers said.
Insurgent attacks have decreased sharply in Iraq since the height of insurgency, but recent spikes in attacks amid months-old Sunni protests against the Shiite-led government have raised fears that sectarian killings could gain momentum across the country.
Alarmed by a nationwide deterioration in the security situation, Iraqi Prime Minister Nouri al-Maliki has ordered a reshuffle in senior military ranks.