The deadliest attack took place tonight when a car bomb exploded on a commercial street in Baghdad's western district of Mansour, killing 10 people and wounding 25, police said.
Security forces sealed off the area, which is often packed with nighttime shoppers.
At least 20 cars were set ablaze by the blast, which damaged several shops and restaurants. Police said four children were among the wounded.
An hour later, a car bombing on a commercial street killed three people and wounded 12 in Baghdad's Amil neighborhood, police said.
Medical officials confirmed the casualty figures. All officials spoke on condition of anonymity as they were not authorized to release information.
Nobody claimed responsibility for the attacks. Baghdad has seen near-daily attacks as security forces struggle to dislodge the Islamic State group from vast areas in northern and western Iraq seized by the extremists during a stunning blitz last summer.