The first explosion, which occurred about 11 a.m., targeted a passing police patrol, killing six people - three policemen and three pedestrians - and wounding nine other people, a police officer said.
At least seven cars also were damaged in the blast, which struck near to the Interior Ministry's nationality and social affairs directorate and the 14th of July bridge in Karradah, he added.
Another parked car bomb about 500 meters (yards) away struck at about the same time, ripping through a bustling market of vegetables and household goods, killing three civilians and wounding five others, the policeman added.
AP Television News footage showed U.S. soldiers milling about the charred wreckage, with shattered glass and blackened debris from nearby shops and street stalls strewn on the bloodstained pavement.
Another car packed with explosives struck a police patrol in Elway square at about 11:30 a.m. in another part of Karradah, killing two policemen and a civilian and wounding five people, police said.
Karradah, a popular shopping area, has been hit by several high-profile bombings, and Monday's attack occurred despite a 5-month-old U.S.-Iraqi security operation aimed at stopping such violence in the capital.
A roadside bomb also was aimed at a police patrol but missed its target, killing a civilian and wounding two others in the southern Shiite area of Hillah, another officer said. Gunmen elsewhere in the province killed a 35-year-old lawyer, he added.
Elsewhere, gunmen opened fire on an open-air market in Iskandariyah, killing a man and his wife as well as a policeman who started firing at them, another officer said.
Three bullet-riddled bodies of men in civilian clothes also were found at a construction site in Iskandariyah, a mostly Sunni Arab city 50 kilometers (30 miles) south of Baghdad, police said. The men, ages 25 to 35, had been bound by their hands and legs and bore signs of torture.
The police officials all spoke on condition of anonymity because of fears they too would become targets.