It was the latest in a series of coordinated attacks targeting civilian areas that has killed hundreds in recent months.
Four police officers said the bombs, placed in parked cars and detonated over a half-hour, targeted commercial areas and parking lots.
The deadliest blasts were in the northern Shaab, southern Abu Dshir and southeastern Nahrwan neighbourhoods, each of which killed six people.
Other blasts hit the neighbourhoods of Mashtal, Baladiyat and Ur in eastern Baghdad and the northern Sab al-Bor and Hurriyah districts.
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There was no immediate claim of responsibility, but such systematic attacks are a favourite tactic of al-Qaeda's local branch.
It frequently targets civilians in markets, cafes and commercial streets in Shiite areas in an attempt to undermine confidence in the government, as well as members of the security forces.
Violence has spiked in Iraq since April, when the pace of killing reached levels unseen since 2008. Today's attacks bring the death toll across the country this month to over 500, according to an Associated Press count.