The deadliest attack was a blast near a police headquarters and hospital in eastern Baghdad. The US military said that explosion killed 18 people, including five Iraqi police officers, and wounded 21.
Half an hour earlier a truck bomb rammed the security barriers outside the Australian embassy, witnesses said. Two Iraqis were killed and two Australian soldiers were among several people wounded, officials said.
Australian ambassador Howard Brown said the truck bomb that exploded near his embassy was close to residences for diplomatic security personnel.
"It was a car bomb aimed at the building where the security people are based. It was quite a substantial explosion," he said.
National Guard headquarters
A third vehicle bomb killed two Iraqi security guards near Baghdad's international airport, and a fourth killed two civilians and two Iraqi soldiers at a military complex in Baghdad, the US military said.
Iraqi journalist Ziyad al-Samarai told Aljazeera the third explosion targeted the biggest headquarters of the Iraqi National Guard in central Baghdad.
Soldiers examine the scene after
the Australian embassy bomb
A bomber drove through the southern gate of the former al-Muthanna airport - now a military base - and blew up his vehicle at the checkpoint, al-Samarai said.
Five people were injured and taken to the al-Yarmuk hospital in Baghdad.
A police source said another bomb also exploded at a Baghdad bank, targeting police as they collected their salaries. Witnesses said at least one person was killed.
Resistance fighters have repeatedly targeted Iraqi soldiers and police in the run-up to the elections with bombings and ambushes.
Iraqi forces are to provide protection at polling stations on election day.
On Tuesday, Iraq's US-backed interim government announced a range of measures to try to prevent bloodshed during the ballot, with land borders to be closed for three days and vehicles barred from getting close to polling stations.