There was no immediate claim of responsibility for the attacks, but insurgent groups, mainly al-Qaida and other Sunni militants, frequently target civilians in cafes and public areas, as well as members of the Iraqi security forces, in an attempt to undermine confidence in the Shiite-led government and stir up Iraq's already simmering sectarian tensions.
Monday's bombings were the latest episode in a wave of violence that has roiled Iraq since a security crackdown in April on a protest camp in a northern Sunni town.
The attacks started with in the town of Beiji, a former insurgent stronghold 250 kilometers (155 miles) north of Baghdad, where a suicide bomber rammed his explosives-laden car into the main gate of the town police station.
That explosion paved the way for three other suicide bombers, who were on foot, to storm inside and blow themselves up in the building, a police officer said. Eight policemen, including an officer, were killed while five were wounded in the attack, he said.
Later in the morning, several bombings hit different parts of Baghdad and northern Iraq, killing 30 people and wounding 73, police said.
The deadliest of the attacks in the Iraqi capital was in the southeastern Bayaa neighborhood, where a parked car bomb ripped through a parking lot, killing six civilians and wounding 12.
Another parked car bomb went off in the central Salhia neighborhood near the heavily fortified Green Zone where key government offices and foreign embassies are located. That attack killed five civilians and wounded 14.
Four civilians were killed and 11 were wounded when a parked car bomb exploded at an outdoor market in Baghdad's central Sadriyah neighborhood. A bomb went off near a bus station in the nearby al-Nahda area, killing three people and wounding seven. Another bomb in the eastern suburb of Hussainiyah killed one civilian and wounded seven.
And two other civilians were killed and seven wounded in a car bomb explosion in the southeastern suburb of Jisr Diyala.
Also Monday, gunmen opened fire on a bus in Mosul that was carrying Shiite pilgrims traveling to the holy Shiite city of Karbala, killing seven people, including four women, and wounding eight. Mosul is located about 360 kilometers (225 miles) northwest of Baghdad.
In the northern city of Tikrit, some 130 kilometers (80 miles) north of Baghdad, three suicide bombers set off their explosives belts in a bid to break into the building of the city council. Two civilians were killed in that attack and seven were wounded.
Medical officials confirmed the casualty figures. All officials spoke on condition of anonymity because they were not authorized to talk to media.
Monday's bombings came a day after militant attacks killed at least 20 people in Iraq. At least 262 people have died in attacks across the country so far this month, according to an Associated Press count.
Associated Press writers Qassim Abdul-Zahra and Sameer N. Yacoub contributed to this report.