Most of the violence on Wednesday occured in Diyala province just north of the capital around the city of Baquba, where 10 people were killed and three more bodies found, according to police sources.
In the north-western city of Mosul, where armed fighters have conducted a campaign against government security forces, a bomber detonated his explosive vest at a police checkpoint outside a courthouse.
Six officers were wounded, but the bomber was the only person killed in the attack, city police said.
In the north-eastern city of Kirkuk, two civilians were shot dead in a carjacking and two more, including a child, were wounded in a shootout between anti-government fighters and troops at an army checkpoint, Captain Imad Jassim said.
Meanwhile, on the road between Basra and Nasiriya in the country's south, a remote-controlled roadside bomb tore apart a civilian car, killing the driver and his passenger, police said.
Iraqi police also found six more bodies under a bridge between the two volatile cities of Mahmudiya and Latifiya, south of Baghdad.
Officers said they appeared to have been killed some time ago.
Meanwhile, police in the southern Shia town of Amara said that an Iraqi army officer had been killed by a pistol shot in front of his home, while a former member of ousted leader Saddam Hussein's Baath party was also murdered, police said.
British forces arrested six
alleged fighters in Amara
Amara has been tense since a raid by a British armoured column on Tuesday netted six alleged fighters suspected of shelling a nearby army base, including one described by a British spokesman as a "significant terrorist".
In the capital, Baghdad, one civilian was killed when a roadside booby-trap ripped open a minibus, and two bomb attacks - including a car bomb - wounded nine police officers, an interior ministry official said.
One of the bombs was apparently aimed at Jawad al-Bulani, Iraq's interior minister, who was travelling through the Dura district in an armoured car in a convoy of about 10 vehicles.
Al-Bulani was not hurt, but the blast injured two bystanders, including a 12-year old, and wounded five traffic policemen, said Dura police officer Mohammad al-Baghdadi.
US and British commanders have expressed their cautious optimism that a plan to restore peace to Baghdad was working.
On Tuesday, Major-General William Caldwell, a US spokesman, said: "We are always very cautious not to take just two weeks' of data and make a long-term assessment on it ... but the initial indications are very positive."
Lieutenant-General Rob Fry, the commander of British troops in Iraq, praised the Baghdad operation in a video-conference with reporters in Washington.
"I think that what we've seen in Baghdad over the last four or five weeks has been an extremely well-conceived operation that tries to combine military effect with political engagement," he said.