The shootings and explosions, which also wounded 85 people, were the latest in a spate of violence in the past week that has broken a relative calm, even though authorities had announced moves to boost security during the four-day Eid break.
UN special envoy Martin Kobler condemned Saturday's violence as "atrocious," adding in a statement: "The targeting of worshippers is an appalling crime."
Saturday's deadliest attacks were in Baghdad, where 15 people were killed.
In the Shia bastion of Sadr City, northeast Baghdad, twin bombings killed at least nine people and wounded 32 others on Saturday evening, officials said.
And in the east Baghdad neighbourhood of Maamal, a bomb exploded in a market as women were shopping for groceries alongside their children at around 9:00 am (0600 GMT).
At least five people were killed, including three children and a woman, security and medical officials said, adding that 13 others were wounded.
An AFP journalist at the scene reported pools of blood along the street, and pieces of shrapnel mixed with vegetables scattered on the ground.
Just north of Baghdad in the town of Taji, a magnetic "sticky bomb" attached to a minibus ferrying Shia pilgrims killed at least five people and wounded 12, officials said.
They said some Iranian pilgrims were among the dead and wounded, but it was unclear how many. Differing tolls and details of casualties are common in the chaotic aftermath of attacks in Iraq.
Two attacks in the predominantly Shia town of Muqdadiyah killed two people and wounded five others, meanwhile, and eight people were wounded by a car bomb targeting a Shia Muslim religious foundation's offices in the town of Tuz Khurmatu.
Shia Muslims in Iraq typically use the Eid holiday, which began on Friday, to visit relatives, the graves of dead family members or shrines of key figures in Shia Islam across the country.
In the run-up to the holiday, authorities in several provinces, including Baghdad, announced tightened security, apparently to no avail.
While no group has yet claimed responsibility for the attacks, Sunni militants frequently target Shia pilgrims during Muslim holidays such as Eid or Shia commemoration ceremonies.
In Mosul, 350 kilometres (220 miles) north of Baghdad, three attacks targeting the tiny Shabak community killed five people and wounded 10, officials said.
In separate shootings, gunmen burst into the homes of Shabak families and killed a total of five people, and wounded four others including young children, while a bombing in the compound of a family home wounded six.
"The security forces are supposed to be responsible for protecting all the citizens of Mosul," said Qusay Abbas, a Shabak member of the provincial council of Nineveh, of which Mosul is the capital.
"This is a very troubling attack."
The Shabak community numbers about 30,000 people living in 35 villages in Nineveh, and many want to become part of the autonomous Kurdish region of northern Iraq.
They speak a distinct language and largely follow a faith that is a blend of Shia Islam and local beliefs.
The community was persecuted under former Iraqi dictator Saddam Hussein, and after the 2003 US-led invasion they were targeted several times by al Qaeda.
Levels of violence have declined dramatically in Mosul and nearby towns and villages, but the city that was once an al Qaeda stronghold is widely cited as one of the places where the network's Iraqi front still holds sway.
In a mostly Sunni neighbourhood of west Baghdad, meanwhile, twin blasts killed a policeman and wounded five others.
The death toll from Saturday's violence was the highest since 33 people were killed in nationwide attacks on September 30.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ