The bodies were riddled with bullets and their hands and feet were tied in what appeared to be death-squad killings, a police official said.
The victims - aged between 20 and 50 years old - showed signs of torture. Their bodies were dumped in several areas around the capital.
A bomb outside a bakery in the mainly Sunni neighbourhood of Dora killed 10 people and wounded at least four.
Police said a large homemade bomb had been placed under the baker's car.
On Tuesday, government officials announced that all security checkpoints in Baghdad would soon be manned by an equal number of Shia and Sunni troops, in an effort to ensure that the security forces do not allow sectarian attacks.
The decision is part of a new four-point security plan announced by Nuri al-Maliki, the prime minister, intended at uniting the divided parties behind security efforts to stop the killings.
Al-Maliki's plan, which was unveiled a week ago, called for the creation of local Shia-Sunni committees that will oversee policing in each district of Baghdad, reporting back to a central committee for peace and security to co-ordinate with the security forces and the prime minister.
Each side has accused the other of backing armed militias, and Sunnis in particular say that the Shia-dominated police force often allows militias to carry out kidnappings and murders.
The central committee will meet in the next few days to work with the interior and defence ministries on arranging the new checkpoints.
Outside the capital, the brother of a Baghdad police brigadier was found shot dead, tied to a lamp post in Buhriz, 60km north of the capital, police said.
Later, the body of another of the brigadier's brothers was discovered in the street.
While in the northern city of Mosul, a police colonel was killed in a drive-by shooting as he walked through the city, police said. A civilian was also killed in a second drive-by shooting.
Three other shooting victims were found, two in Khalis, 80km north of Baghdad, and the third in Baquba, police said.
Two Iraqi soldiers were killed by a roadside bomb during a foot patrol in Musayyib and another was shot dead near Hillah.
In Amara, a former member of Saddam Hussein's Baath party was shot and killed by unidentified assailants, police said.