The bloodiest attack occurred at lunchtime on Wednesday when a man wearing an Iraqi army uniform blew himself up at a base in Khales, northeast of the capital, security sources said.
Twenty-three people were killed and 29 wounded, most of them soldiers, local council member Samira Shibli said.
Hours later, eight policemen were killed and vehicles left ablaze in a second attack, when a bomber targeted their patrol in southern Baghdad, security sources said.
Aljazeera reported that several British soldiers were wounded in an explosion followed by clashes in eastern Baghdad.
Five civilians also died and six were wounded when two mortar rounds slammed into a north Baghdad neighbourhood later on Wednesday.
In northern Iraq, a mortar attack killed seven Iraqis, including two policemen and a woman, in the town of Tal Afar, police said.
Another 15 people were wounded as the mortar round landed close to police headquarters.
Iraqis gather at the scene of a
car bomb in southern Baghdad
The al-Qaida-linked group of Jordanian fighter Abu Musab al-Zarqawi claimed responsibility for the canteen attack, in an internet statement whose authenticity could not be verified.
"Our brother was invited to lunch. We pray to God that he finished his meal in paradise," it said, adding that the attack was carried out to avenge the detention of women prisoners by Iraq's Interior Ministry and US-led forces.
Iraqi soldiers killed
edical sources in Falluja said a number of Iraqi army soldiers had been killed and others wounded when three explosive devices blew up in different parts of the town.
The explosions destroyed one military vehicle and damaged another.
In al-Tuz, north of Baghdad, an officer in the Rapid Deployment Force, Brigadier Nafie al-Bayati, was killed and two officers wounded when their convoy was attacked by armed men.
North of Baghdad, an explosive device detonated near a US patrol. US troops used a helicopter to transport the wounded to hospital.
And in the northern town of Biji, unidentified assailants blew up an oil pipeline that linked Kirkuk's oilfields to the al-Dura refinery
Against the backdrop of the Khales army canteen attack, Aljazeera interviewed an expert on Iraq's security and military affairs, Mohamed al-Askari, a retired brigadier.
Iraqi security forces come under
Asked if the fighters are adopting new strategies in their attacks on police patrols and sites close to military bases, al-Askari said: "Certainly they are adopting new strategies to counter the government's security plan. For, now they face more difficulties in reaching their targets.
"The ongoing attacks are, however, not a result of negligence on the part of Iraqi security forces. The Iraqi forces are on alert and are carrying out military operations. The assaults are still occurring because the fighters have succeeded in infiltrating the ranks of the security forces and have insiders cooperating with them."
"Similar was the case of the the attack that took place a week ago at the headquarters of al-Zieb Brigades, where a bomber detonated his explosives."
"The restaurant where Wednesday's bombing occurred was very close to a military base, possibly a part of it. This is why I believe the security set-up had been penetrated and meticulous planning went into the execution of attack against what was an extremely difficult target," he said.
Al-Askari said: "The government's security offensive has largely succeeded. But the lapses that are occurring from time to time indicate that the fighters have their own ways to spring surprises and get around obstacles."