An official at the Interior Ministry said at least 43 people were killed and 76 others wounded in the bloodiest attack in the capital in recent weeks.
The official added that the casualty figure is likely to rise, saying charred bodies are "all over the place."
The first two of the attacks occurred at a busy bus station. The third was close to a hospital as victims of the earlier blasts were being taken there.
Ahmad Jabur witnessed the two first explosions. "We heard an explosion in the garage," he said. "We went there and ran towards the buses for Al-Kut, Al-Basrah, and Al-Amarah. As we were evacuating the wounded from the station, a second car bomb exploded at the entrance near a police pickup truck and a GMC vehicle. It exploded in the middle of the police cars."
Near the northern city of Kirkuk, six Iraqi soldiers were killed hen insurgents opened fire at their car.
The blasts come two days after politicians failed to meet a deadline to draft a new constitution for the country due to disagreement on several key issues -- namely the role of Islamic law, federalism, and the sharing of natural resources.
On 16 August, Iraqi Prime Minister Ibrahim al-Ja'fari vowed the draft constitution will be finished by the new deadline
of 22 August.
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