At least two bombs exploded in crowded street markets, killing at least five people and wounding more than 30, an interior ministry spokesman said.
American forces said they had killed a leading member of Al Qaeda but the death toll was mounting despite a large-scale security operation.
Attackers gunned down Jassim Mohammed al-Dahabi, the dean of Baghdad's College of Economics and Administration, along with his wife and son, in an unexplained early morning attack that was condemned by senior officials.
"We demand that security forces take action to protect academic and scientific institutions and not just stand by in the face of this plot against us," the ministry of higher education said.
Meanwhile, insurgents shot dead three police officers manning a checkpoint in the commercial heart of the city and set off a bomb in a popular butchers' market, killing one person and wounding 22 more, medics said.
In another attack, a motorcycle bomb was detonated in the flashpoint Sadr City district, killing four people and wounding eight, said interior ministry spokesman Brigadier General Abdul Karim Khalaf.
Explosions continued to rock the central district of Baghdad near the defence and interior ministries and the Green Zone, the heavily fortified home of the embattled Iraqi government and the US embassy.
Sports officials said the coach of Iraq's disabled handball team and a player -- both members of Baghdad's Sunni minority -- had been kidnapped by gunmen from their gym during a training session in central Baghdad.
The gang arrived in two jeeps, burst in and asked for the two men, Khalid Najimaldin, the team's 48-year-old able-bodied coach, and Issam Khalaf, a 33-year-old blind player, witnesses and sports officials told AFP.
Najimaldin tried to resist the attackers, and was badly beaten, while the building's sole guard was powerless to resist the gang, said Tayeh al-Nuaymi, chairman of the Iraqi Paralympic Committee.
Insurgents murdered 12 people, including three police, in separate attacks in and around the strife-torn town of Baquba, north of Baghdad, police said.
Further north, in the restive oil city of Kirkuk, gunmen murdered Amal Ahmed, a pharmacist and former army officer, as she headed to her shop -- one of a series of attacks on female professionals by suspected militants.
Sarkot Hikmat Shawkat, a policeman from the city's Oil Protection Police, was cut down in a drive-by shooting, said police Captain Imad Jassim.
The US military confirmed a soldier had died on Wednesday after being hit by a roadside booby trap in Baghdad, becoming the 2,817th military casualty since the US-led invasion of March 2003.
Another US soldier, 41-year-old Iraqi-American reservist Specialist Ahmed Qusai al-Taie, was named on Thursday by a US spokesman as the kidnap victim being searched for by 2,000 US and 1,000 Iraqi troops.
But US forces and their Iraqi allies also reported two successes in the battle to restore control of Iraq to Prime Minister Nuri al-Maliki's fragile and beleaguered national unity government.
Iraqi and US officials said that six donkeys had been intercepted carrying smuggled weapons -- 53 anti-tank mines and an anti-tank rocket -- across the border from Iran, which has been accused of arming Shia militias.
And in the city of Ramadi, an Al Qaeda stronghold in western Iraq, US warplanes on Wednesday fired laser-guided bombs at a car carrying a senior insurgent chieftain, killing him and his driver, the US military said.
"Rafa Abdul Salam Hamud al-Ithawi, also known as Abu Taha, was the emir of Shamiyyah," it said. "He frequently harboured foreign fighters who entered Iraq illegally in order to assault innocent Iraqis and coalition forces."
Ramadi has become the focus of the battle between US forces and Sunni Arab insurgents fighting under the Al Qaeda banner. Last week a US spokesman said marines had launched an offensive to take back the city.
On October 15, Al Qaeda militants held a brief parade in central Ramadi to declare the region an independent emirate, scoring a propaganda victory, but fierce fighting has continued since.
Ramadi residents said Abu Taha had been a notorious bandit sentenced to 90 years in jail under the ousted regime of Saddam Hussein, only to be released by the regime shortly before the US-led invasion in a bid to stoke chaos.
He became one of the most powerful Al Qaeda emirs in Ramadi, controlling up to half the city, they told AFP.

Copyright AFP (Agence France-Presse), 2006