The attacks were the latest in a surge of unrest that has left more than 4,200 people dead this year.
The evening car bombings struck various parts of Baghdad, including the centre and the northeast, killing at least 21 people, most of them civilians, and wounding 87, security and medical sources said.
Earlier in the day, a provincial official was shot dead in the capital.
Near the main northern city of Mosul, gunmen ambushed a vehicle carrying unarmed policemen and raked it with machinegun fire, officials said.
A separate attack west of Mosul left a soldier dead.
In Fallujah, west of the capital, militants wearing explosive belts attacked a police station and traded fire with security forces.
Three of the bombers were killed when their explosives blew up while a fourth militant was shot by police, officials said, adding that 12 policemen were wounded, including two officers.
Authorities insist a campaign targeting militants is yielding results with hundreds of suspects captured and dozens more killed.
They say security forces have also dismantled a number of insurgent training camps and bomb-making sites.
Analysts and diplomats say militants have exploited the minority community's disenchantment to recruit new fighters and carry out attacks.
The surge in violence comes as the government grapples with a prolonged political stalemate, with no significant legislation passed since March 2010 parliamentary elections.
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