The bombs in the capital city targeted a hospital, a restaurant and markets in Shiite neighborhoods, The New York Times reported.
At least 30 people were killed and more than 100 wounded in the Baghdad bombings, authorities said.
Officials said they tightened security in the city, fearing more attacks.
Two car bombs killed three people and injured 15 in Basra in southern Iraq.
A bomb in Muthanna province killed six people and injured 19.
In Kut, southeast of Baghdad, two car bombs left six people dead and about 20 injured.
There was no immediate claim of responsibility for any of the attacks, Voice of America reported.
The United Nations has said more than 2,500 Iraqis have died in attacks throughout the country since April, the BBC reported. More than 700 of those people have been killed in July.