Police officers said bombs placed in parked cars in commercial areas and car parks across Baghdad were detonated within a half hour of each other, killing 42.
Additionally, a suicide bomber targeted a group of soldiers in the northern city of Mosul, killing 14 including five civilians.
The deadliest Baghdad attack was in the south eastern Nahrwan district, where two car bombs exploded simultaneously, killing seven and wounding 15 others.
Two other explosions hit the northern Shaab and southern Abu Dshir neighbourhoods, each killing six people. Car bombs were also detonated in Mashtal, Baladiyat and Ur in eastern Baghdad, Bayaa in the south west of the city and the northern Sab al-Bor and Hurriyah districts.
The attack in Mosul took place when the bomber drove an explosives laden car into a group of soldiers who were closing off a road. As well as the deaths, at least 30 people were injured, a police officer said.
Co-ordinated car bomb attacks have regularly hit Iraq over the past year, and have killed more than 5,000 people since April.
The approach is a favoured tactic of al-Qaeda in the area, though no-one has claimed responsibility for Sunday’s attacks.
It is estimated that more than 500 people have been killed this month in such attacks.
Shia Muslims are often the target of such attacks. Shia Muslims are the majority religious group in Iraq.