Bombings have hit two markets in Baghdad province, killing at least 23 people, while armed men have killed five members of one family south of the capital, officials say.
Three bombs went off simultaneously in the Shia village of Sabaa al-Bour, about 30 kilometres north of the Iraqi capital.
Police said the explosions, two at the market entrance and one inside the shopping area, went off as the place was packed with shoppers, killing 16 people and wounding 41 there.
Three women and two children were among those killed in the village market, according to police and hospital officials. Several shops and cars were damaged in the blast.
The attack came shortly after a bomb blast hit the al-Athorien market in Baghdad's southern neighbourhood of Dora. Police said that seven people, including two women, were killed in the Sunni area and 17 people were wounded.
Armed groups in Iraq often bomb areas where crowds of people gather, and have struck markets, football pitches, cafes, mosques, weddings and funerals.
South of Baghdad, assailants killed on Thursday a man said to have been a former fighter from the anti-Qaeda Sahwa (Awakening) movement, his three sons and one of their cousins.
The Sahwa, who helped US forces from late 2006 to bring about a sharp reduction in violence, are frequently targeted by Sunni armed groups, who consider them traitors.
Separately, a magnetic "sticky bomb" on a car killed a policeman and wounded two civilians in the northern city of Mosul.
A similar device killed an employee of a local television station and wounded a second in Baquba, also north of Baghdad.
Iraq is experiencing its worst violence since 2008, when it was emerging from a brutal sectarian conflict, and more than 250 people have been killed in just seven days.
Elsewhere on Thursday, a bomb killed a man and wounded his brother in Kirkuk while two alleged al-Qaeda fighters were killed by armed men west of the city.
The identity of the assailants was not immediately clear, but armed groups affiliated with al-Qaeda and those from the rival group Ansar al-Sunnah have traded attacks in recent weeks.
Thursday's violence came a day after attacks in northern Iraq, including assaults by armed men on local government and police buildings, killed 33 people.
There are persistent fears of a return to the all-out Sunni-Shia sectarian violence that peaked in 2006-2007 and killed tens of thousands of people.
The UN Refugee Agency said this week it was "increasingly concerned about the situation in Iraq, where recent waves of sectarian violence threaten to spark new internal displacement of Iraqis fleeing bombings and other attacks".
About 5,000 Iraqis have been displaced this year, joining more than 1.13 million who had previously fled or been forced from their homes, it said.