Authorities had hoped violence could be avoided over the holiday of Eid ul-Azha.
At least 30 people have been killed in a series of attacks around Iraq, with dozens more injured.
Twin bomb attacks in Baghdad's mainly Shia neighbourhood of Sadr City on Saturday evening killed at least 13.
Hours earlier, a bomb near a playground in the Bawiya neighbourhood of the capital killed several people, including at least three children.
Authorities had put security measures in place to try to prevent attacks over the four-day holiday of Eid ul-Azha.
Another bomb exploded near Baghdad on a bus carrying Shia pilgrims, some of whom are reported to be Iranian.
Shabak attacked
"Nobody expected this explosion because our neighbourhood has been living in peace, away from the violence hitting the rest of the capital," Bawiya resident Bassem Mohammed told the Associated Press news agency.
"We feel sad for the children who thought that they would spend a happy time during eid, but instead ended up getting killed or hurt," he added.
In the northern city of Mosul, gunmen burst into the homes of families belonging to the Shabak minority group, leaving several dead.
The Shabak are a minority in northern Iraq who have previously been the target of sectarian violence.
Several people were also injured when a bomb exploded in a Shia neighbourhood in the town of Tuz Khurmatu, north of Baghdad.
Violence in Iraq is down since the height of the insurgency in 2006 and 2007, but is still common. In recent months the rate of attacks has increased, mostly targeting security services and Shia Muslims.
In August, more than 90 people were killed in a wave of attacks before Eid ul-Fitr, which marks the end of the holy month of Ramadan.
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