The incidents are the latest in a months-long surge of violence that has raised fears that the country is slipping back toward the widespread sectarian killings of 2004-2008.
Police officials said the deadliest of today's incidents came when four suicide bombers stormed a headquarters for police commandos in the city of Beiji, killing seven policemen and wounding 21 others.
Guards killed one suicide bomber while the three other bombers were able to set off their explosive belts inside the compound, said the police. Beiji, a centre for oil refining, is 250 kilometres (115 miles) north of Baghdad.
In other violence, gunmen shot and killed two prison guards after storming their houses in a village near the city of Mosul early today.
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Also in Mosul, two soldiers were killed and four others were wounded when a roadside bomb struck their convoy. Mosul, 360 kilometres (225 miles) northwest of Baghdad, is a former militant stronghold.
Medics in nearby hospitals confirmed the casualty figures. All officials spoke on condition of anonymity because they were not authorised to speak to media.
More than 4,000 people have been killed between April and August, UN figures show. Another 396 have been killed so far in September, according to an Associated Press tally.
Today's violence comes as voters in the northern Kurdish autonomous region cast ballots in local elections for the Kurdistan Regional Government's 111-seat legislature.
Iraqi Kurds are looking to bolster their autonomy while insulating their increasingly prosperous enclave from the growing violence roiling the rest of the country.