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 is mounting despite a large-scale security operation.
A US military spokesman Major General William Caldwell said that total levels of violence have fallen since the end of Ramadan last week, with casualties down 23 percent and attacks in Baghdad down 41 percent.
Slipping into chaos
The latest attacks have targeted key members of Baghdad society and popular gathering places, striking further blows against reconciliation and reconstruction in an already bitterly divided country.
Assassins 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.
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 bomb was detonated in the flashpoint Sadr City district, killing four people and wounding eight, said interior ministry spokesman Brigadier General Abdel Karim Khalaf.
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.
In other separate incidents, insurgents murdered 12 people, including three police, 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 Islamists.
Weapons seized
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 Shiite 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.
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.