Eyewitnesses said at least one of the bombers struck a US convoy, although there were no immediate reports of American troops among the casualties.
Firefighters tried to douse the flames near one blast site that targeted Iraqi troops in the north of the city, where several cars were destroyed and blood-soaked survivors argued with police.
"The (Iraqi) army vehicles were parking right here when a speeding Daewoo car approached and exploded. It split in two parts," eyewitness Raed Salman said.
A police source said six people were killed and 16 hurt in that blast. The bodies were too charred to immediately identify how many were Iraqi soldiers and how many civilians.
In the New Baghdad district in the southeast of the city, eyewitness Basim Mohammed said he saw a car bomber ram an armoured US convoy at high speed, but he saw no casualties.
Another bomb struck near Andalus Square in the town centre.
Reuters correspondents in central Baghdad heard that blast, followed by gunfire.
An Interior Ministry source said the blast was caused by a car bomb that wounded five Iraqi soldiers and three civilians.
He said there were two other apparent car bombs, near an old Defence Ministry headquarters and near a US patrol in east Baghdad. He had no reports of casualties on either site.
A US military spokesman said he was checking the various reports.