In the deadliest attack, a suicide bomber detonated an explosives-rigged truck at the checkpoint leading to southern Baghdad, killing at least 20 people and wounding at least 53.
Security officials said the suicide bombing was the only attack in the area, while a medical official said a car bomb also hit shops in nearby Yusifiyah also contributed to the toll.
And an explosives-rigged vehicle detonated on Baghdad's Palestine Street near a tent serving refreshments to Shiite pilgrims, hundreds of thousands of whom will travel to Karbala, south of Baghdad, for the Ashura commemorations, which peak on Tuesday.
But with the Islamic State (IS) jihadist group -- which considers Shiites heretics and frequently attacks them -- in control of large areas of Iraq, the danger is even greater this year.
There are tents serving water and tea to pilgrims across the capital, and the main route to Karbala, the shrine city where Imam Hussein is buried, passes through the checkpoint that was bombed today.