In the northern oil city of Baiji, a suicide bomber driving a fuel tanker killed 18 people and wounded 40 in an attack on a police headquarters in the city.
In the other attack, a suicide car bomb killed eight people and wounded 25 in the Shi'ite city of Al-Hillah, south of Baghdad.
Reports say the attack took place near the governor's office in the city, and next to a police academy building. Police officers were among the dead.
And in a third attack, a suicide bomber blew himself up in a crowded hotel lobby in Baghdad, killing at least seven people.
Earlier, the U.S. military said U.S. and Iraqi forces had discovered what appeared to be an Al-Qaeda-run "execution house" in the town of Ba'qubah.
A statement said soldiers searching the house found five bodies buried in the yard behind the building and bloody clothes in several rooms inside it.
It said a nearby house had been converted into an illegal prison with several numbered rooms and bars covering the windows. Several blindfolds were found inside.
(compiled from agency reports)