In the deadliest attack, a suicide bomber detonated explosives inside a restaurant in east Baghdad's Jadida area, killing 12 people and wounding more than 30, said security and medical officials.
There was no immediate claim of responsibility for the attack, but suicide bombings are almost exclusively carried out by Sunni extremists in Iraq, including the Islamic State jihadist group.
IS spearheaded a sweeping offensive in June that overran large areas north and west of Baghdad, and Iraqi forces are now battling to push the jihadists back.
Another attack – said to have been either a suicide or roadside bombing – hit a commercial area in central Baghdad, killing at least five people and wounding at least 13.
Saturday's attacks illustrate the persistent danger of violence in Baghdad even as the nightly curfew was set to end at midnight in the city.
Lifting the curfew is a major change to a longstanding policy aimed at curbing violence in the capital by limiting movement at night, which has failed to stop frequent bombings.
Prime Minister Haider al-Abadi ordered the move this week, a decision his office said was taken so there would "be normal life as much as possible, despite the existence of a state of war".
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