No group immediately claimed responsibility for the attacks but the bombings bore the hallmarks of an al-Qaida-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 U.S. troops.
The deadliest of the day's attacks took place in the town of Numaniyah, about 80 kilometers (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. In all, five people were killed and 17 were wounded, police said.
Earlier in the day, a car bomb in Baghdad's central Nidhal Street killed four people and wounded 11, while three people died and nine were wounded in a car bombing in the northern Kazimiyah district.
Car bombs also exploded in the areas of Shaab, Shammaiya, Karrada and Maamil, killing a total of seven people and wounding 30, police officials added.
Later Wednesday, three more civilians died and eight were wounded when another car bomb struck Baghdad's central upscale commercial area of Jadiriyah.
Medical officials confirmed the causality figures. All officials spoke on condition of anonymity because they were not authorized to talk to the media.
Violence has surged in Iraq since last year, with the country weathering its deadliest bout of violence since it pulled back from the brink of civil war in 2008. U.N. figures showed that last year, Iraq saw the highest death toll in attacks, with 8,868 people killed.
Wednesday's attacks came as Iraq is heading toward a crucial election on April 30, its first vote since the 2011 U.S. troop pullout.
More than 9,000 candidates will vie for 328 seats in parliament but there will be no balloting in parts of the western, Sunni-dominated Anbar province engulfed in clashes between security forces and al-Qaida-inspired militants.
On Tuesday, the country's Independent High Electoral Commission said those areas were too dangerous for the vote to take place.
Since late December, the western Anbar province has seen fierce fighting between government troops and allied tribal militias on one side, and militants from the Islamic State of Iraq and the Levant, an al-Qaida spin-off group, on the other.
The militants have seized and are continuing to hold parts of the provincial capital, Ramadi, and nearly all of the nearby city of Fallujah.
Associated Press writer Sinan Salaheddin contributed to this report from Baghdad.