No-one claimed responsibility for the attacks, but they bore all the hallmarks of al-Qaeda and other Sunni militant groups.
The bombings were the latest incidents in a wave of violence that has rocked Iraq since a security crackdown in April on a protest camp in a northern Sunni town.
They started with an attack in the town of Beiji, a former insurgent stronghold 150 miles north of Baghdad, where a suicide bomber rammed his explosives-laden car into the main gate of the town's police station.
The blast paved the way for three other suicide bombers, who were on foot, to storm inside and blow themselves up in the building. Eight policemen were killed and five wounded.
Later, there were several bombings across Baghdad which killed 21 people and wounded 58, police said.
The deadliest of the attacks in the Iraqi capital was in the southeastern Bayaa district, where a bomb in a parked car killed six civilians and wounded 12.
Another car bomb went off in the central Salhia neighbourhood near the heavily fortified Green Zone, killing five civilians.