The bombings -- particularly in the city of Amarah, which has largely avoided such attacks -- appeared aimed at jarring the country's Shiite majority.
Many were alarmed last week by scenes of armed Sunni men battling Iraqi forces around the country and the announcement of a Sunni tribal army to defend the western Anbar province against the Shiite-led government.
There is now widespread fear of a sustained insurrection in the country's Sunni-dominated western and central regions.
Monday's bombings were certain to stoke worries that, if a war erupts, even regions with a Shiite majority will not be spared bloodshed.
In Amarah, at least eight people were killed and 18 wounded in two car bombings near a market where municipal employees gather before work, security officials said.
"The first exploded in a place where the cleaners used to gather every day," said Ali Kadhim Raheem, who lives near the site of the blasts. "Some women serving breakfast were killed. Some shoppers were hurt. Several shops were destroyed."
A car bomb also exploded in a market in the center of Mahmoudiya, just south of Baghdad, leaving four dead and 14 wounded, security officials said.
In the southern Shiite shrine city of Karbala, a car bomb blew up in a factory area, leaving two dead, officials said. Another car bomb exploded near a restaurant in Diwaniyah, also in the south, killing eight people and wounding 25, according to officials.