Nine separate explosions targeted markets and busy shopping streets and took place as residents celebrated the Eid holiday.
One of the bombings was near an outdoor market in the southeastern suburbs of the capital shortly before sunset, killing seven people and wounding 20.
Outside Baghdad, a suicide bomber detonated a bomb in a car on a busy street in the town of Tuz Khurmato, 105 miles north of the capital, killing at least 10 people and wounding 45, medical and police sources said.
Tuz Khurmato is located in a particularly violent region over which both the central government and autonomous Iraqi Kurdistan claim jurisdiction.
Police believe the bomber was trying to reach the local headquarters of a Kurdish political party, but was unable to reach the building because of increased security in the area, a police source said.
There has been a surge in violence in Iraq since the start of the year.
More than 1,000 people were killed in July, the highest monthly death toll since 2008 amid worries of a return to the all-out sectarian war that blighted Iraq years ago.
Sunni Islamist militants have been regaining momentum in their insurgency against the Shi'ite-led government.
And they have been emboldened by the civil war in neighbouring Syria, which has stoked sectarian tensions across the Middle East.(Courtesy:X FM London)