Sunday's attacks coincided with the announcement that Iraq's parliament will meet on Thursday for the first time since the December elections.
It was one of the worst days of violence in Baghdad in recent months.
An official said 50 had been killed and 290 wounded in the Sadr City blasts. "We expect the toll to rise," the official said.
Two car bombs exploded in one market while a third blew up almost simultaneously at another in Sadr City. Police said they had found a fourth car bomb in a third market and defused it.
"People were torn to pieces," a witness said at the scene of one blast. "Nobody knows the number of casualties. It's a lot, it's a lot."
Sadr City is a stronghold of Shia leader Muqtada al-Sadr, who commands al-Mahdi Army militia. The district in eastern Baghdad has been relatively free of violence in the last couple of years.
The predominantly Sunni Iraqi Islamic party has denounced the bombings in al-Sadr city in a statement, saying that the bombings were intended to complicate the political situation and impede the talks for the formation of a new Iraqi government.
Iraq has been gripped by a spasm of sectarian bloodletting after the bombing of an important Shia mosque in Samarra on 22 February. But in recent days, there had been a relative lull in violence, prompting officials to declare the crisis was over.
A Reuters reporter said there were chaotic scenes at a hospital in Sadr City where many of the casualties were admitted. Some wounded were lying on the floor, others on stretchers. One woman wept as a man slapped his head in grief.
Sadr City had not seen violence
in the past two years
The toll was sure to rise as residents, many firing machine guns in the air, raced to and fro to collect charred corpses from among burning vehicles and shops.
Residents kicked the head of the bomber, an African, as it lay in the street of the Hay market in the east Baghdad neighbourhood.
Sirens wailed as ambulances raced to and from the scene. Smoke billowed into the air and fires continued to burn. Many shops were demolished by the explosions.
Before the Sadr City bomb blasts, rocket and gunfire killed at least 12 people including 10 in Baghdad, and wounded 27.
Elsewhere in Baghdad, US forces were waging a battle against Iraqi fighters in a western neighbourhood.
Police said the fighting erupted at about 3pm in Khadra.
An AP Television News cameraman reported that a US helicopter landed nearby to evacuate casualties.
It was not known what prompted the fighting, or if there were any dead. There was no immediate comment from the US military.
Also on Sunday, six Iraqis were killed and 13 wounded when a roadside bomb exploded near a US army patrol near the airport, on the western outskirts of town.
Sadr City is the stronghold of
Shia leader Muqtada al-Sadr
There was no immediate word from US forces on possible American casualties, but Raafar al-Bayati, an Iraqi journalist, told Aljazeera that one US soldier was also killed in the attack.
Earlier, two civilians were killed and six wounded when a mortar shell landed on a house in central Baghdad, and two more civilians were hurt when another shell fell in an east Baghdad street.
Three other civilians in a car were shot dead by unidentified armed men in the south of the capital, near the industrial zone in al-Bayaa district.
Two newly recruited Iraqi intelligence officers, Ghassan Ali al-Samarrai and Hamid Salih al-Janabi, were killed while they were driving a car in al-Jamiaa neighbourhood in western Baghdad.
Five Iraqi soldiers were wounded when their vehicle was hit by a roadside bomb in the centre of town.
Two policemen were wounded by a roadside bomb in Dura, in the south of the city while two men, one a policeman, were shot and killed by unidentified assailants in Duluiya, 75km north of the capital.
Meanwhile, an Iraqi group affiliated to al-Qaida in Iraq said on Sunday it was behind Saturday's killing of a senior editor for Iraq's state television.
Hamid was the second Iraqi
journalist to be killed in one week
A statement posted on the internet said: "Your brothers in the military wing of the Mujahidin Council assassinated on Saturday Amjad Hamid, the editor of Iraqiya ... which always broadcasts lies about jihad to satisfy Crusader masters."
The statement, attributed to the group, said the station was "the mouthpiece of the apostate government".
The authenticity of the statement could not be verified, but it was posted on a website often used by hardline groups.
Armed men killed Hamid along with his driver as they headed to work in Baghdad. He was the second Iraqi journalist to be killed in a week.