The level of violence in Iraq has fallen since the peaks of 2006 and 2007, but bomb attacks remain commonplace.
An interior ministry official said at least 95 people were killed and more than 563 injured in Wednesday morning's apparently co-ordinated attacks.
Two huge bombs - believed to have been hidden in trucks - went off, sending plumes of black smoke into the sky.
The biggest blast was near the foreign ministry, just outside the Green Zone. It was powerful enough to break windows at the parliament building inside the zone, which houses government and diplomatic buildings.
It also left a crater 3m (10ft) deep and 10m in diameter, with the smouldering wreckage of cars scattered around the site of the explosion.
"The windows of the foreign ministry shattered, slaughtering the people inside," Asia, a ministry employee, told Reuters news agency.
"I could see ministry workers, journalists and security guards among the dead," she said.
Minutes earlier, another blast close to the finance ministry in another hitherto relatively safe area of the city is reported to have affected a raised highway nearby.
At least four other explosions went off in other parts of Baghdad, including the Bayaa district of southern Baghdad.
Several mortars fell inside the Green Zone itself.
"Everybody on the street was going crazy," Mustapha Muhie, who works near the Green Zone as an administrator, told the BBC's Newshour programme.
"Everybody was just trying to get to their cars, just trying to get home - and that's what I did."
The wave of explosions occurred just as Prime Minister Nouri Maliki was about to arrive at a nearby hotel to hold a news conference, which was cancelled.
Later, in a statement, Mr Maliki said Iraqi security forces were "very capable of confronting terrorists", but also called for a security review.
"The criminal operations that happened today no doubt call for a re-evaluation of our plans and our security methods to face the terrorist challenges," he said.
There have been no claims of responsibility for the bombings.
Past attacks have been blamed on al-Qaeda linked-Sunni insurgents.
Natalia Antelava BBC News, Baghdad
These are unusual attacks - in the last few weeks, we have seen explosions in Baghdad, but these attacks occurred in some of the supposedly safest neighbourhoods of the city.
For many people, these attacks confirm their worst fears over the withdrawal of US troops from cities across Iraq at the end of June and handing over of the security situation to Iraqi forces. A lot of people before the withdrawal were saying they were very fearful that attacks would rise.
The government said they were in full control - but attacks like these, in what should be a very safe, very well-protected area of Baghdad will certainly shed some very serious doubts on these assurances.
An Iraqi army spokesman said two al-Qaeda members had been arrested in a Baghdad district in connection with the attacks.
Iraqi President Jalal Talabani said the attackers were "trying to rekindle the cycle of violence of previous years by creating an atmosphere of tension among the Iraqi people".
The violence comes exactly six years after one of the first major attacks in Iraq after the toppling of Saddam Hussein.
On 19 August 2003, the UN headquarters in Baghdad was hit by a suicide truck bomb, killing 22 people in what was the most deadly attack up until that point since the US-led invasion earlier that year.
Tens of thousands of Iraqis have been killed in the violence that followed.
The anniversary was chosen for the UN's inaugural World Humanitarian Day, in an effort to increase support for aid workers.
UN Secretary-General Ban Ki-moon said he was "saddened" by Wednesday's "appalling" attacks.
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