A roadside bomb in the north of the city killed a civilian and wounded six others as they were heading towards Karbala to mark the religious rite of Ashura.
At least one civilian was killed in an explosion that hit pilgrims in southern Baghdad.
"A bomb exploded on the main road in Zaafaraniya district, killing a Shia pilgrim and wounding eight others," a security official confirmed.
Two police officers were killed and three others wounded in a similar bombing in Iskandariya, 40km south of Baghad, police said.
In Mosul, a bomb attack targeted a US-Iraqi military patrol and left one Iraqi soldier dead.
The violence that erupted in Iraq after the 2003 invasion has decreased in the past year, but suicide attacks still take place.