The polls are the country's first since the departure of US troops in late 2011, and they see Prime Minister Nuri al-Maliki seeking a third term.
But the election has been overshadowed by attacks on candidates, election workers and political rallies, and parts of the country that have been out of government control for months will not see any ballots cast.
In west Baghdad, an attacker wearing a suicide belt targeted a polling station early today as security force personnel queued to vote, killing seven people and wounding 15, a police colonel said.
After the blast, police shut off the road and ambulances rushed to and from the scene of the attack, an AFP correspondent said.
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Soon after that attack, a suicide bomber targeted a polling centre in Tuz Khurmatu north of Baghdad, killing three policemen and wounding seven, the town's mayor said.
In the northern city of Kirkuk, a suicide bomber detonated his belt at a voting station, killing six policemen and wounding nine, according to a high-ranking security official.
Elsewhere in Kirkuk, a roadside bomb targeting an army convoy killed one soldier and wounded two.
Also in Mosul, six journalists were wounded when a roadside bomb blast hit their bus as they were on their way to cover the voting by members of the security forces.
And near Ramadi, west of Baghdad, a soldier was killed when his convoy travelling to a polling station was targeted by a roadside bomb, security personnel said.