As many as 10 suicide bombers carried out the attacks, which reportedly targeted members of the security forces and allied Shia Muslim militias.
The Islamic State (IS) group, which holds territory in the north and west, said it was behind some of the attacks.
In the deadliest attack, at least 14 people were killed when a bomber blew himself up in a restaurant.
The eatery was popular with members of the Popular Mobilisation, a predominantly Shia militia which has taken a lead role in the fight against IS, the Associated Press reports.
Other attacks hit the southern city of Basra, Baghdad and Mashada, north of the capital.
In recent months government forces backed by Shia militias and US air strikes have regained control over significant parts of Iraq from IS.
On Sunday, the army said it had made progress in an offensive to recapture the western city of Hit, which has been under IS control for the last 18 months.
It said it had taken the northern edge of Hit, about 140km (85 miles) from Baghdad, but was being slowed down by the presence of hundreds of roadside bombs planted by IS.

The 26-year-old, who has been linked with a move to Real Madrid, fractured his right ankle while on international duty with Belgium on Sunday.
Chelsea said the operation on Monday was "successful", but that Hazard will not return to training for approximately three months.
The new Premier League season is due to begin on 12 August.
Hazard will also miss pre-season games against Arsenal, Bayern Munich and Inter Milan in Singapore from 22-29 July, and the Community Shield against Arsenal on 6 August.
Hazard was instrumental as Chelsea won the Premier League last season, scoring 16 goals in 36 games.

Two-year-old Lane Thomas Graves had been playing in the sand near the resort's Seven Seas Lagoon when he was dragged underwater by the creature.
His parents and older sister had been visiting the Grand Floridian resort in June 2016 from the state of Nebraska.
The lighthouse has been installed near to where the attack occurred.
Wildlife officials classified the killing as a predatory attack, saying the boy did nothing to provoke the alligator.
"He was in the water not more than ankle deep," the Florida Fish and Wildlife Conservation Commission said in a report, describing how the boy had been gathering water for a sandcastle.
His father, Matt Graves, jumped in the water to try to pry open the creature's mouth, but "the alligator thrashed and broke Matt's grasp and went under the water," according to the report.
A Disney spokesperson said they hoped the monument would spread awareness for the Lane Thomas Foundation, which also uses the lighthouse as its logo.
Who is liable for alligator boy's death?
"The lighthouse sculpture has been installed to help spread awareness of the Lane Thomas Foundation, which was established to provide assistance and support to families whose children need organ transplants," Walt Disney World said in a statement.
After the death, Disney was criticised for not having posted signs warning of the danger along the man-made lagoon, which borders Magic Kingdom.
Public notices have now been added to the area, Florida media report.
The Lane family announced a month after the boy's death that they would not sue Disney, and would instead "solely be focused on the future health of our family".
At least 25 people have been killed and dozens wounded in bomb attacks across Iraq, media reports say.
[NEXT_CONCEPT]
Chelsea forward Eden Hazard will miss the start of the Premier League season after having surgery on a broken ankle.
[NEXT_CONCEPT]
Walt Disney World has unveiled a lighthouse memorial for a young boy who was killed by an alligator while on holiday at the Florida theme park.