Baghdad police said the first blast struck a bus and taxi stop around rush hour in the eastern Sadr City neighbourhood.
Nine people were killed, including a 7-year old child, and 16 were wounded, two officers said.
Another car bomb hit a small market at a taxi stop in the eastern suburb of Kamaliya, killing three civilians and wounding 14 others, they said.
In the northern city of Mosul, a suicide attacker rammed his car into an army check point, killing two soldiers and wounding three others, another police officer said.
Mosul is located 360 kilometres northwest of Baghdad.
In Baghdad's southwestern neighbourhood of Baiyaa, drive-by shooters shot and killed a brother of a Sunni lawmaker and wounded two of his guards, two other police officers said.
Four medical officials in a nearby hospital confirmed the causality figures. All officials spoke on condition of anonymity because they are not authorised to brief reporters.
The attack followed a wave of bombings yesterday that struck in mainly in Shiite neighbourhoods, killing 33 people.
At least seven of them died in Sadr City when a bomb in a parked car detonated at a bus stop.
No one immediately claimed responsibility for yesterday's and today's attacks, but car and suicide bombings are a hallmark of al-Qaeda's Iraq branch.
The spike in attacks, after a general decrease in violence, has raised fears of a return to the sectarian bloodshed that pushed the country to the brink of civil war in 2006-2007.
