Security officials and a medic at the Ibn Nafis hospital in Baghdad said that at least seven people, including three policemen, were killed and another 30 were wounded in the second attack.
In the third incident, a car packed with explosives struck a police patrol in Elway Square, also in Karrada, killing three people and wounding five.
Five Iraqi soldiers were also killed by a roadside bomb near the border with Iran.
Lieutenant Muntadhar Mohammed said that the bomb targeted the soldier's patrol between the towns of Badra and Bela Druz, 180km east of Baghdad.
"All the five members of the patrol were killed in the early morning attack," he said.
In the southern city of Amara, armed men shot dead a former Baath party member, police have said.
Gunmen also killed a man and wounded his wife when they shot at the couple's car on a highway near the town of Iskandiriya, south of Baghdad.
Another policeman was killed in an armed assault at a police checkpoint in central Iskandiriya. Iraqi police have also found the bodies of three men who were tortured and shot dead in the eastern part of the town. It was not known when they were killed.
Police also reported that Zaydan al-Shammari, a lawyer, was shot dead by gunmen in the city of Hilla.