The bombing at the Shurja market killed 24 people and injured 35, police said.
Other blasts and shootings left at least 14 dead in the Iraqi capital, while in Hilla, a bomb killed 12 men queuing to join the police.
The Baghdad blasts come amid a joint US-Iraqi security clampdown that officials insist is working.
The top US general in Iraq, George Casey, said on Wednesday he could see Iraqi forces taking on responsibility for the country's security within 12 to 18 months, with "very little" coalition support.
But Baghdad's citizens probably do not feel the security clampdown is working, says the BBC's world affairs correspondent Nick Childs.
Attacks in pictures
The latest bombings, particularly in the capital, he says, look like further attempts by insurgents in a political war of nerves to disprove US and Iraqi assertions.
A roadside bomb went off at the Shurja market, a teeming maze of shops and stalls, at about 1000 local time (0600 GMT), when it was full of shoppers and traders, police said.
"There are patches of blood everywhere in the area and firefighters are fighting to quell the fire, as many shops are burning," a police officer told the French news agency AFP shortly after the explosion.
Shurja is one of the country's best-known markets and attracts buyers and sellers from all over Iraq.
It has been attacked before. A blast there three weeks ago left 10 people dead.
In other violence:
At about 0800 (0400 GMT) on Wednesday, men were queuing at the recruitment centre in Hilla, 120km (75 miles) south of Baghdad, to apply for police jobs when a bomb exploded.
The device had been left in a parked bicycle, a police spokesman said.
Recruitment centres for the Iraqi army and police have been frequent targets for insurgents.
Hilla, the capital of the mixed Sunni and Shia province of Babel, has been frequently targeted by insurgents.
It was the scene of the bloodiest single attack in Iraq since the US-led invasion in 2003, when about 125 people were killed by a suicide bomber in February 2005.
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