Hundreds of Shi'ites were marching toward a mosque when a bomb killed a number of people and injured many more in Khanaquin, northeast of Baghdad.
In the nearby town of Mandali, a suicide bomber blew himself up at the gate of a Shi'ite mosque.
And gunmen ambushed a bus carrying Shiite pilgrims to a mosque in Baghdad.
This witness says the attack hit a minibus as it passed through the Dora neighborhood, near a gas station.
Two carloads of armed men drove by the bus and opened fire.
This year's Ashura ceremony takes place at a time of heightened sectarian tensions between Sunni and Shi'ite Muslims. Thousands of Iraqi soldiers and police are deployed to protect nearly two million Shi'ite Muslim pilgrims observing Ashura in the city of Karbala.
Tens of thousands have died in a cycle of attack-and-revenge shootings and bombings since a bomb wrecked a key Shi'ite mosque in Samarra last February.
Ashura is one of the holiest times on the Shi'ite calendar and it recalls the death of Imam al-Hussein. He was the Prophet Muhammad's grandson and died battle in 680 A.D. near Karbala. His death cemented the split in Islam between Shi'ites and Sunni Muslims.
Observances include processions and ceremonies, including self-flagellation, in a show of grief to mark Hussein's death in battle.
There were also observances in one of Baghdad's Shi'ite neighborhoods, where men dressed in white beat drums as they walked in processions through the streets.
The ceremonies also include reciting religious texts.
Meanwhile, Iraqi officials say the leader of an Islamic cult that was plotting to assassinate senior Shi'ite clerics during Ashura, died Sunday in fighting near Najaf. Cult members included heavily-armed Muslims from both the Sunni and Shi'ite branches of Islam.
An Iraqi spokesman said more than 200 militants died in the fighting, and more than 100 were captured.