At least 10 people were killed when two car bombs blew up near a bus station in the city of Kut, 150 kilometers (95 miles) southeast of the capital, police said.
Four more died in a blast in the town of Mahmoudiya, about 30 km (20 miles) south of Baghdad.
The rest of the bombings took place across Baghdad, in Sadr city, Habibiya, Hurriya, Bayaa, Ur, Shurta, Kadhimiya and Risala neighborhoods.
A relentless campaign of bombings and shootings has killed nearly 4,000 people in Iraq since the start of the year, according to violence monitoring group Iraq Body Count.
The violence has raised fears of a return to full-blown conflict in a country where Kurds, Shi’ite and Sunni Muslims have yet to find a stable way of sharing power.
In recent months, Sunni Islamist militants have regained momentum an their insurgency against the Shi’ite-led government, striking with a ferocity not seen in years.
In July alone, more than 810 people have lost their lives in militant attacks.
Sectarian tensions across the region have been inflamed by the civil war in neighboring Syria, which has drawn Shi’ites and Sunnis from Iraq and beyond into battle on opposite sides.