One of the attacks, which took place in the predominantly Shi'ite Muslim district of Bayaa in Baghdad when a bomb in a parked vehicle detonated near car workshops, killed seven and wounded 14.
Accorrding to United Nations, violence in Iraq is at the highest level in at least five years and the capital has been targeted almost daily. More than 8,000 have been killed this year.
Sunni insurgents, mostly with links to al Qaeda, have claimed several large bombings in Iraq this year. The last large set of bombings was on November 21 north of the capital. Since then, there has been a steady flow of smaller attacks.
No group immediately claimed responsibility for Sunday's bombings but al Qaeda has increased its grip on areas across the country since the escalation of the crisis in neighbouring Syria and the withdrawal of U.S. troops from Iraq in 2011.
At least 94 people were wounded in Sunday's attacks. In one, a car bomb exploded in a busy square in central Baghdad, killing at least five people and wounding 15, police said.
In Radhwaniya, a predominantly Sunni area in the capital, a roadside bomb killed two people and wounded eight, police said.
There were other attacks in Baghdad's mainly Shi'ite districts of Amel, Ghadir, Sadr City and Hussainiya.
In Baquba, 65 km (40 miles) northeast of Baghdad, a bomb in a parked car blew up inside a market killing two people and wounding seven, police said.