The first two blasts went off ten minutes apart in the capital, Baghdad.
Five minutes later, a third car bomb exploded in the southern holy city of Karbala.
Meanwhile, Iraqi police announced they had found the handcuffed bodies of 43 men who had been shot in the head in apparent sectarian attacks in Baghdad.
In a separate incident, at least four British soldiers were killed when their helicopter crashed in the Iraqi city of Basra, triggering riots in which at least five Iraqis were killed, including one child.
British soldiers have cordoned off the crash site and imposed a night time curfew.
According to Iraqi police, the helicopter ploughed into a residential area of Basra's central Al-Rabbat district after being hit by a rocket.
British ground troops moved in to recover the crew and were set upon by local people.
Two British tanks and a Land Rover were set on fire and shooting broke out between civilians and British troops.
Iraqi police said five local people, including two children, were killed.
Another 28 people were wounded.
The British military claimed troops did not fire directly into the crowds but fired live rounds at targets threatening them.
One AFP correspondent on the scene reported that the Iraqis fired rockets at British vehicles.