Coordinated bombings hit Iraq multiple times each month, feeding a spike in bloodshed that has killed more than 5,000 people since April.
The local branch of al-Qaeda often takes responsibility for the assaults, although there was no immediate claim for today's blasts.
Today's attacks were the deadliest single-day series of assaults since October 5, when 75 people were killed in violence.
The deadliest blasts struck in the southeastern Nahrwan district, where two car bombs exploded simultaneously, killing seven and wounding 15, authorities said. Two other explosions hit the northern Shaab and southern Abu Dshir neighbourhoods, each killing six people, officials said.
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Other blasts hit the neighbourhoods of Mashtal, Baladiyat and Ur in eastern Baghdad, the southwestern Bayaa district and the northern Sab al-Bor and Hurriyah districts.
Meanwhile, in the northern city of Mosul, a suicide bomber drove his explosives-laden car into a group of soldiers as they were sealing off a street leading to a bank where troops were receiving salaries, killing 14, a police officer said. At least 30 people were wounded, the officer said.
The former insurgent stronghold of Mosul is located about 360 kilometres northwest of Baghdad.
In the afternoon, a bomb blast killed four people and wounded 11 inside an outdoor market in the Sunni town of Tarmiyah, 50 kilometres north of Baghdad, authorities said.
Such coordinated attacks are a favourite tactic of al-Qaeda's local branch.
It frequently targets civilians in markets, cafes and commercial streets in Shiite areas in an attempt to undermine confidence in the government, as well as members of the security forces. All of the car bombings today in Baghdad struck Shiite neighbourhoods.