Police officials said the deadliest of the attacks took place at night when a car bomb exploded near a market in Baghdad's northeastern district of Shaab, killing 10 people, including three policemen, and wounding 13 others.
A car bomb also exploded in a commercial street in northwestern Baghdad, police said, killing five people and wounding 14.
Another car bomb killed four and wounded 12 in a commercial street in Baghdad's Hurriyah neighbourhood, police said.Earlier, another car bomb exploded in a commercial street in northern Baghdad, killing three people and wounding 13 others.
Near the city of Fallujah, army artillery shelled a village overnight, killing four civilians, hospital officials said. Medics in nearby hospital confirmed the death toll for all attacks.
Meanwhile, the UN chief Ban Ki-moon arrived in Baghdad on a visit aimed at discussing regional issues, especially the crisis in Syria. Ban expressed deep concern over the violence hitting Iraq's Sunni-dominated Anbar province.
"The situation in Anbar Governorate, particularly in Fallujah and Ramadi, is a source of grave concern. The security situation in Iraq is undoubtedly a source of great concern," he told reporters during a joint Press conference with the Iraqi Prime Minister Nouri Al Maliki.