The worst attack came 30 kilometers (20 miles) south of the capital in Mahmudiyah where a car bomb exploded in the center of a popular market killing six people and wounding another 26, security sources said.
In nearby Iskandriyah, another bomb exploded in a residential area killing a man and his 13-year-old son.
Baghdad city was the scene of several mortar attacks, including one on the health ministry, which is controlled by followers of Shia cleric Moqtada al-Sadr, in which three people were killed five wounded, a security source said.
At nearly the same time, a car bomb exploded near the Nida mosque in the northern Sunni stronghold of Adhamiyah, killing one person.
Another mortar attack in downtown's Jumhuriyah Street killed another person and wounded eight.
Not long afterwards, a pair of mortars fell on Kadhimiyah neighbourhood, a Shia stronghold home to two holy shrines, and killed two people and wounded eight.
Duelling mortar salvos between rival neighbourhoods has become an increasingly common manifestation of the capital's instability.
Wednesday's attacks came after the late night suicide bombing of a Shia cafe in north Baghdad in which 17 people were killed and 20 wounded.
The attacks mark the first major violence in the capital since the lifting of a two-day curfew imposed during the sentencing to death of Saddam on Sunday for crimes against humanity.
In the wake of the verdict there were demonstrations both for and against the sentence around the country.
Baghdad, like other parts of Iraq, is riven by sectarian violence that claims around 100 victims a day.

Copyright AFP (Agence France-Presse), 2006