The US military also announced the deaths of three of its servicemen, taking its total losses since the March 2003 invasion to 2,662, according to Pentagon figures.
A soldier was killed on Wednesday in the western city of Ramadi, while another died in the northern town of Hawija and a marine was killed in the Al-Anbar province.
In the worst attack, a suicide attacker killed 12 policemen and wounded 39 people, when he detonated a car bomb near a Baghdad police fuel depot, interior ministry spokesman Brigadier General Abdul Karim Khalaf said.
"Eighteen vehicles were destroyed, of which 12 were civilian cars and the rest belonged to the police," he added.
In another attack, insurgents killed three civilians and wounded 17 people in a roadside bombing near a Sunni mosque in northeast Baghdad, he said.
The attack targeted a police patrol near al-Nida mosque in the largely Shiite al-Qahira neighbourhood, which has been the site of numerous attacks in the past few weeks.
Two more people were killed in a double bombing in Amel, in south Baghdad.
Insurgents also set off a car bomb near a police commando checkpoint close to the central Baghdad Tayran Square on the way to the interior ministry, killing three police and five civilians and wounding 30 people, Brig Gen Khalaf said.
Fresh violence flared in the restive southern neighborhood of Dura, which was once one of the most violent places in the capital until it
became the focus of joint US-Iraqi military operations.
Two police were killed during a mission against insurgents while four others were injured in a separate incident involving a roadside bomb.
There were also a number of attacks in predominantly Sunni western Baghdad, which has also been a centre of government efforts to pacify the city.
A woman and a soldier were killed and nine people were wounded in three attacks in the Yarmuk neighborhood.
In the upscale Mansur district, also in the west of the city, a civilian was killed when a roadside bomb went off near a restaurant, while four people were wounded in a second bombing in the area.
Three others were wounded in another roadside bombing near Baghdad's Al-Mustansiriyah university, the security official added.
Insurgents have managed to carry out attacks in Baghdad despite a security crackdown in the capital since June 14.
In northern Iraq, a police officer was killed and four wounded by a roadside bomb east of the oil city of Kirkuk, while gunmen assassinated a leader of the defunct Baath party in Hawija, west of the city.
Gunmen clashed with a police patrol in the northern city of Tikrit, in which a policeman and a civilian were killed, according to Salaheddin police.
Northeast of Tikrit, gunmen in cars descended on a police patrol, killing three and wounding four. Also in the north, a former lieutenant colonel in the Saddam-era army was shot dead, police said.
In the restive province of Diyala, north of Baghdad, four Iraqis were killed in separate attacks and a Shiite shrine was destroyed by a bomb made of TNT and gas cannisters, police said.
A civilian died when his vehicle struck a roadside bomb in Balad Ruz, while two others were killed in separate shootings in the provincial capital of Baquba, where gunmen also set fire to 12 shops in a market, police said.
In several grim discoveries across the country, 19 bodies were recovered, security sources said.
The latest string of bombings came ahead of Thursday's ceremonial start of a handover of Iraq's military command from the US-led forces to Iraqi authorities.