According to Al Alam reporter, explosions occurred on Monday in Sabaa al-Bour, al-Baladiyat , al-Kadhiliya, al-Shart al-Rabeia, and Sadr City.
At least 42 people have died in the attacks, according to Reuters.
The deadliest attack took place in Sadr City, where a car bomb blew up near a place where workers had gathered. It killed at least seven people, including two soldiers.
It was not immediately clear who carried out the attacks, but radical militants have been stepping up their insurgency and striking with a ferocity not seen in years.
More than two years of insurgency in neighbouring Syria have caused fresh violence in Iraq.
Shi'ites, security personnel government employees of both sects and Sunni "Sahwa" militia members are prime targets for al-Qaeda and the extremist insurgents.
On Sunday, a suicide bomber blew himself up inside a mosque where a funeral was being held, killing at least 40 people in Mussayab, 60km (40 miles) south of Bagdad.
The United Nations mission in Iraq said about 800 Iraqis were killed in acts of violence in August.
SHI/SHI