The day's first explosion took place in Baghdad outside the offices of al-Sabah, a state-owned daily newpaper, at about 9am (0500 GMT) on Sunday.
The suicide car-bomber killed two people and wounded 18 people - mainly newspaper employees.
The explosion also destroyed nearly 20 cars owned by the newspaper's staff. The publication's offices were also partly damaged.
Karim al-Rubaiya, head of al-Sabah's technical department, said: "Thank God the blast took place early in the day. There were fewer casualties as many employees had not reached the office yet. Part of the building collapsed."
Al-Rubaiya said that guards at the car park fired at the vehicle "which the bomber was attempting to drive fast in the parking lot. As the guards fired at him, he blew up the van."
Iraqi militant groups have frequently attacked journalists and particularly reporters from Iraq's state-owned media who many Sunnis believe unfairly favour Iraq's ruling Shia parties.
Central Baghdad explosion
A second explosion occured when a bomb planted in a minibus was detonated outside a hotel in central Baghdad, killing at least nine people and injuring 20.
The bomb exploded shortly before noon outside the Palestine Hotel near an entrance. The attack caused a fire.
The minibus was reportedly heading to Kerrada, a mainly Shia and Christian district of Baghdad.
The blasts occurred despite a recent security operation by thousands of American and Iraqi troops to bring peace to the capital.
Blast targets Kurds
A third bombing in the northern Iraq city of Kirkuk killed one Kurdish security guard when a suicide bomber exploded a lorry full of explosives outside the offices of the Patriotic Union of Kurdistan, one of the two main Kurdish parties.
A few minutes later the Kurdish guards of a nearby Kurdish office shot and killed a man driving a car packed with explosives.
A boy receives treatment
after the al-Sabah blast
Kirkuk, an ethnically mixed town, has experienced increasing violence over the last few months as its Kurdish majority accelerates efforts to remove Arab settlers from the city and surrounding areas.
There were several other attacks around Baghdad on Sunday.
A bomb planted inside a food market killed at least five people and wounded 15 in the town of Khalis, 80km north of Baghdad.
Gunmen killed two brothers and their cousin in Abara, just north of Baquba, 65km north of Baghdad.
Mahmoud Faisal, a lieutenant-colonel in the Iraqi army, was killed in the town of Muqdadiya, 90km northeast of Baghdad.
Police in Baghdad also said on Sunday that they had found the bodies of 20 people who had been tortured and then killed.