Attacks on anti-Qaida fighters earlier in the day claimed another five lives.
The attacks are the latest in a surge of bloodshed that has roiled Iraq for months, heightening worries that the country is returning to the widespread sectarian killing that marked the years following the 2003 US-led invasion.
Police reported casualties from explosions in eight different neighbourhoods.
The force of one powerful blast, a car bomb explosion in the Bab al-Sharji neighbourhood that killed three and wounded 11, rattled windows in central Baghdad.
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Car bombs also hit the mainly Shiite neighbourhoods of Zafaraniyah, with four killed and 11 wounded, Alam, with two dead and 10 wounded, Obeidi, with two killed and eight wounded.
Confessionally mixed neighbourhoods were also hit. A roadside bomb hit a commercial street in Kam Sarah, killing three and wounding eight, and the eastern Baghdad al-Jadidah, killing three and wounding 17.
Another car bomb exploded in shopping streets in the mainly Sunni neighbourhood of Dora, killing four and wounding eight, and in the mostly Sunni area of Sadiyah, killing three and wounding 10.
There was no immediate claim of responsibility, but coordinated bomb blasts in civilian areas are a frequent tactic by al-Qaida's Iraq arm.
Earlier, al-Qaida claimed responsibility for a spate of rare suicide attacks last month in the northern, relatively peaceful self-ruled Kurdish region, underlining the terror group's growing strength across the country.
The Sept 29 twin suicide car bombs hit a complex housing the regional Interior Ministry and other security agencies in Irbil, the capital of the Kurdish region, killing at least six Kurdish troops and wounding more than 30 others.