The deadliest attack hit the northern Shaab neighbourhood, where a car bomb followed by a suicide blast killed 19 people, security and medical sources said.
Car bombs and suicide attacks targeting mainly Shi'ite Muslim districts of Baghdad killed 35 people on Sunday, one of the heaviest recent tolls in the Iraqi capital, which has faced a wave of bombings by Islamic State militants.
The deadliest attack hit the northern Shaab neighbourhood, where a car bomb followed by a suicide blast killed 19 people, security and medical sources said. The car exploded near a crowded market and, as police and bystanders gathered, an attacker detonated explosives strapped to his body.
In Bunouk district in the capital's northeast, a bomb in a car killed nine people, the sources said. Security forces were sweeping areas nearby, some with sniffer dogs, after receiving information about two further possible bombs, they said.
More than 100 people were wounded in the three explosions.
There was no immediate claim of responsibility, but Islamic State militants who control much of northern Iraq and the province of Anbar west of Baghdad regularly send bombers into the capital.
Earlier on Sunday, a suicide bomber killed five people in Kadhimiya neighbourhood, home to one of Shi'ite Islam's holiest shrines, shortly before dusk and the end of the daily Ramadan fast. Another bomb in the Iskan district of western Baghdad killed two people, medical sources said.