It is the latest bout of violence ahead of the country's first parliamentary elections since the 2011 US troop withdrawal.
No group claimed responsibility for the attacks but they bore the hallmarks of an al Qaeda-inspired group and other Sunni insurgents, who use suicide and car bombs to target public areas and government buildings to undermine confidence in the Shi'ite-led government.
The explosions also coincided with the anniversary of the 2003 fall of Baghdad in the hands of US troops.
The deadliest attacks took place in Numaniyah, about 50 miles south of Baghdad, where a bomb first went off in a busy commercial area, followed by a car bomb that exploded as people gathered to help the victims from the first blast.
Altogether, five people were killed and 17 were wounded.
Earlier in the day, a car bomb in Baghdad's central Nidhal Street killed four people and wounded 11.
Three people died and nine were wounded in a car bombing in the northern Kazimiyah district.
Car bombs exploded in the areas of Shaab, Shammaiya, Karrada and Maamil, killing seven and wounding 30.