In the deadliest incident at least eight people were killed after a car bomb exploded near a market in Mahmudiya, south of Baghdad, police sources said.
Earlier, at least four people died and several were wounded after a car bomb went off next to a minibus in Baghdad's Kamaliyah neighbourhood.
In Baquba, north of Baghdad, gunmen fired on a minibus, killing five passengers and injuring four, police said.
Seven labourers in the northern city of Mosul were killed by unidentified gunmen, possibly because they worked for the police department, local police said.
The US military also said four marines were killed in two separate combat incidents in the Anbar province on Saturday.
Meanwhile, US forces on Sunday killed five suspected fighters and detained five others in a raid on a house southwest of Baghdad.
One woman died and three women and a child were injured in the pre-dawn swoop for an al-Qaeda operative in Yusifiyah.
The US military said in a statement: "During the assault, five terrorists, three of them wearing suicide vests, were killed; five others, one of whom was wounded, were detained.
"Two of the suicide bombers were killed before either could detonate their vest, and the third detonated his body bomb killing only himself."
The US military added that their forces came under fire from the house as they approached it before returning fire themselves.
One of the five detained was the al-Qaeda operative alleged to be involved in setting roadside bombs and operations involving foreign fighters.
In the southern city of Basra one British soldier was also killed and three others injured in a bomb attack, the BBC reported on Sunday.
The attack took place on Saturday afternoon at Shaibah military base.