No group immediately claimed responsibility for the attacks but the bombings bore the hallmarks of an al-Qaeda-inspired group and other Sunni insurgents, who frequently use suicide and car bombs to target public areas and government buildings in their bid to undermine confidence in the Shiite-led government.
The explosions also coincided with the anniversary of the 2003 fall of Baghdad in the hands of US troops.
Earlier in the day, a car bomb in Baghdad's central Nidhal Street killed four people and wounded 11, while five people died in a car bombing in the northern Kazimiyah district.
Car bombs also exploded in the areas of Shaab, Shammaiya, Karrada, Maamil and Sadr City, killing a total of 13 people and wounding 42, police officials added.
Mortars also fell on the village of Sabaa al-Bour, about 30 kilometres north of Baghdad, killing 4 civilians and wounding 13, police said.
Medical officials confirmed the causality figures. All officials spoke on condition of anonymity because they were not authorised to talk to the media.