The blasts targeted markets and car parks in mainly Shia Muslim districts of the city.
There has been a recent upsurge in sectarian violence, sparking fears of a return to the bloodletting of 2008.
More than 5,000 people have been killed so far this year, according to United Nations data.
Monday’s blasts struck during Baghdad’s morning rush hour, with reports of 13 bombs, most of them in Shia neighbourhoods.
Groups of labourers gathering ahead of the working day were among the bombers’ targets.
One of the deadliest attacks was reported from the eastern Sadr City district where seven people were killed and 75 injured in a crowded vegetable market.
Another six were reported killed in Shuala, a mainly Shia area of north Baghdad.
The city neighbourhoods affected also included New Baghdad, Habibiya, Sabaa al-Bour, Kazimiya, Shaab and Ur, as well as the Sunni districts of Jamiaa and Ghazaliya, the Associated Press news agency reports.
No-one has claimed responsibility for Monday’s attacks, but Sunni Muslim insurgents have been blamed for much of the most recent violence.
The interior ministry accused rebels linked to al-Qaeda of exploiting political divisions and regional conflicts to sow violence.
“Our war with terrorism goes on,” interior ministry spokesman Saad Maan told AP.
The recent upsurge in violence was triggered in April by an army raid on a Sunni Muslim anti-government protest camp near Hawija, north of Baghdad.
Many in the country’s Sunni Muslim minority complain of being excluded from decision-making and of abuses by the security forces. Recent raids in Baghdad on suspected al-Qaeda hideouts in mainly Sunni districts are thought to have worsened grievances.
One of the bloodiest attacks over the past few weeks was a double bombing in a funeral marquee in Sadr City on 21 September, which left more than 60 people dead.
Several dozen people died in a wave of attacks on Sunday, including another explosion at a funeral.
A suicide bomber attacked a Shia Muslim mosque south of the city, causing the roof to collapse. More than 40 people are now known to have been killed in that incident.
Irbil, the normally stable capital of Iraq’s autonomous province of Kurdistan, was hit by a series of bombings on the same day, killing six members of the security services. Officials said that violence could be linked to fighting between jihadists and Kurds in Syria.