The blasts hit commercial areas in the neighborhoods of Karrada, Baiyaa, Shurta, Tobchi and Zafaraniyah.
They were timed to go off during the breaking of the fast for Ramadan known as iftar when people are out shopping and eating.
The Associated Press quoted a shopowner who works in a neighborhood that experienced the violence: "The evening is the busiest time of day when a lot of people pour into Karrada after iftar to shop or eat in restaurants," the vendor said.
"We don't know who to blame for these security breaches, but we are sure of one thing: Our people are bleeding every day," he said.
More from GlobalPost: Suicide bombers targeting Shias kill dozens in Baghdad
About 250 Iraqis have been killed since the onset of Ramadan, mainly in car bombs and suicide blasts.
Sectarian violence has claimed over 3,000 lives so far this year, according to RFI.
Much of the violence has been caused by Sunnis unhappy with the Shia government. Sunni militant groups have tried to stir unrest and destabilize the government they claim has discriminated against them.
Saturday's violence was no exception, with mainly Shia neighborhoods targeted.
The Associated Press reported that hours before the attack a leader of a Sunni militia was gunned down in a town northeast of Baghdad.
Violence has reached 2008 levels and have sparked fears of a renewed civil war on sectarian grounds.