Ten locations in Baghdad were hit. Many of the dead were Shia pilgrims gathering for a religious festival.
Two blasts near a restaurant in Hilla, south of Baghdad, are thought to have targeted police and security forces.
There has been an upsurge in sectarian violence across Iraq in recent months as political tensions increase.
The first car bomb struck a procession of pilgrims in the town of Taji, north of Baghdad, as they made their way to a shrine for the anniversary of the death of Shia imam Moussa al-Kadhim.
There was then a series of four further blasts across the capital. One tore into a group of pilgrims as they rested at refreshment tents.
A man who witnessed one of the attacks in Baghdad said a car bomb had targeted pilgrims and had also hit people who were working in the city.
"People were slaughtered and killed right here. This wrecked car here belonged to a man who worked to earn his living, and another one belonged to a fuel seller. They could not find his body."
Another man, speaking from his hospital bed in Baghdad, explained what happened.
"A car bomb exploded suddenly. I fell on the ground, then so many people fell on me."
The restaurant that came under attack in Hilla, and where 21 people died, is said to be frequented by police.
A man who owns a restaurant nearby said a car loaded with explosives was detonated when a minibus packed with policemen stopped outside.
"It's heart-breaking. It's just sirens, and screams of wounded people," Maitham Sahib said.
Pictures from the scene showed the mangled remains of a restaurant, damaged cars and roads strewn with debris.
Three bombs exploded in Kirkuk, with one of them targeting the headquarters of Kurdish President Massoud Barzani. One person died and many were injured in that attack.
One man told Reuters: "I want to ask the government, why do they put party headquarters in residential areas and among the civilians? Bombs are still occurring , killing and hurting innocent people."
There are also reports of bombs in Mosul, Balad, and Karbala.
A taxi driver in Karbala told Reuters he was waiting for passengers when the blast took place.
"I flew up into the air, and then down to earth. I started to crawl and I saw people, wounded people scattered on the ground, some of them had their legs ripped off," said Kadhim Hashim.
Violence in Iraq has fallen since the sectarian killings of a few years ago, but militants still frequently attack security forces and civilians.
Extra security and checkpoints have been in place to cope with the thousands of pilgrims who are making their way into Baghdad.
The shrine in the city's Kadhimiya district is the focus of a festival which marks the anniversary of the death of imam Moussa al-Kadhim.
At least four people were killed and 30 injured in a mortar attack near the shrine on Sunday.
Wednesday has been one of the deadliest days of violence since US troops withdrew from Iraq last December.
A series of attacks in January killed 72 people in southern Iraq and Baghdad.
It is not yet known who is responsible for the attacks but Iraqi Sunni insurgents tied to al-Qaeda have attacked Shia targets in the past.
BBC world affairs correspondent Emily Buchanan says sectarian tensions have been simmering since the US withdrawal, and this kind of violence is exactly what they had feared.
Shia Prime Minister Nouri Maliki has been trying to consolidate Shia power at the expense of Sunni and Kurdish voices, she says.
Mr Maliki is currently pursuing an arrest warrant for the Sunni Vice President, Tariq al-Hashemi.
He is accused of funding attacks on government and security officials during Iraq's bloody insurgency.
At the scene
BBC News, Baghdad
It's been another bloody morning - a multitude of car bombs, IEDs and machine-gun attacks.
In Baghdad, policemen and Shia pilgrims - many who had come on foot from across the country - bore the brunt of the assaults, while an employee of a private university was also targeted when his house was bombed.
Soon after the attacks, websites of local political parties critical of Shia Prime Minister Nouri Maliki blamed the political crisis in which Iraq has been embroiled for the past few months.
But Mr Maliki's State of Law coalition pointed the finger of blame at the recent failure of attempts by the prime minister's rivals to topple him with a vote of no-confidence.
Marks anniversary of the death of the 8th Century Imam Moussa al-Kadhim
Said to be buried in a shrine in Kazimiyah, in the north of Baghdad
Each year, a million pilgrims walk to the shrine
In 2005, nearly 1,000 people died when rumours of an attack caused a stampede