In north and south Baghdad, two blasts tore through cafes where scores of young men had gathered to watch a televised football match late on Thursday, killing eight people.
Two other explosions killed 10 people in coffee shops in the city of Baquba, about 50 km (30 miles) northeast of Baghdad, police said.
Another bomb exploded near a cafe in the town of Jbela, 65 km (40 miles) south of Baghdad, killing three, and a "sticky bomb" attached to a car killed a civilian in Iskandariya, 40 km (25 miles) south of Baghdad, police said.
Violence has grown in Iraq since the start of the year, claiming more than 1,000 people in May alone, making it the deadliest month since the sectarian bloodletting of 2006-07.
The latest bombs struck as Iraqis celebrated moves by the UN Security Council towards ending sanctions imposed on Baghdad more than two decades ago after former dictator Saddam Hussein invaded Kuwait in 1990.