The blasts are the latest indication that Iraq's security is rapidly deteriorating as sectarian tensions exacerbated by months of Sunni-led anti-government protests and the war in neighboring Syria are on the rise.
Iraq has been hit by a wave of bloodshed that has killed more than 350 people in the past two weeks alone.
There was no immediate claim of responsibility for today's bloodshed, but the attacks bore the hallmarks of al-Qaeda's Iraqi arm.
The day's deadliest attack happened when two bombs exploded in the eastern Habibiya neighbourhoods, which is near the sprawling Shiite district of Sadr City. That attack killed 12 killed and wounded 35, according to police.
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Twin blasts also struck an open-air market in the predominantly Shiite al-Maalif area, killing six and wounding 12 others, two police officers said.
Another car bomb exploded in the busy commercial Sadoun Street in central Baghdad. It killed five civilians and wounded 14 others, two other police officers said. Among the wounded were four policemen who were in a nearby checkpoint.
Several shops were partially damaged or burned.