The blasts shook the fragile sense of security the capital has maintained despite the Sunni militant offensive raging across northern and western Iraq.
The attacks are among the most significant in Baghdad since insurgents led by the Islamic State in Iraq and the Levant (Isis) captured Iraq’s second-largest city Mosul last month at the start of its blitz across Iraq.
Christians in Mosul, one of the oldest Christian communities in the Middle East, were warned to leave or face death last week in a statement read out in the city’s mosques.
The government has moved aggressively to try to secure Baghdad amid fears it might fall as well, but the deadly bombings have seriously undermined their efforts. The worst took place in the Shiite neighbourhood of Abu Dashir, where a suicide attacker rammed a car packed with explosives into a checkpoint, killing at least nine people and injuring 19. Four policemen were among the dead, a police officer said.
Three car bombs in different areas of Baghdad went off in less than 10 minutes, hitting the districts of Baiyaa, Jihad and Khazimiyah. The attacks killed at least 15 people and wounded another 42. Another car bomb near a bus stop in Khazimiyah killed three people and wounded 15, police said.
The Sunni militant blitz, led by Isis, has pushed into areas west of Baghdad, and also has established a presence in a belt of Sunni areas running south and north of the capital. Baghdad itself has a predominantly Shiite population.
The Iraqi military launched a counter-offensive late last month to try to dislodge insurgents from the city of Tikrit, some 80 miles (130km) north of Baghdad, but Tikrit remains in militant hands.
North-west of Tikrit, heavy fighting has raged around an air base which previously served as a US military facility known as Camp Speicher.
Iraqi military spokesman Lieutenant General Qassim al-Moussawi has denied reports that militants had captured Camp Speicher.
Isis is now fighting also fighting a savage battle Syria after government forces launched a counter-attack to recapture a gas field, with the death toll there over 200.
The fighting in the Shaer field, in the desert region of Palmyra in the central province of Homs, has been among the deadliest battles since the start of uprising.