In the deadliest attack, a suicide bomber killed at least 19 people at the entrance to a Shi'ite mosque in central Baghdad.
More than 30 were reported wounded in that attack.
Elsewhere in Baghdad, bombs went off in the neighborhoods of Sadr City and Dura, killing at least two people and wounding several.
No one immediately claimed responsibility for the attacks.
Violence in Iraq has surged in the past year to its highest level since 2008.
Sunni militant groups often target Iraq's majority Shi'ites.
The United Nations says violence killed nearly 8,900 people in Iraq last year.