The deadliest attack took place in northern Baghdad's mainly Shi'ite district of Shaab where two car bombs went off, killing at least nine people and wounding 25.
No group immediately claimed responsibility for yesterday's attacks but insurgents have been increasing attacks in their fight against the government of Prime Minister Nouri al Maliki.
Islamist militants linked to al Qaeda and tribal fighters have taken control of Ramadi and Falluja, the main cities in the Sunni-dominated province of Anbar, in a serious challenge to the government's authority. Iraqi troops and allied tribesmen are trying to retake the province.
In a separate incident, gunmen set up a fake checkpoint on the main road between Baghdad and Kirkuk, killing six drivers late on Saturday near Udhaim, 60 miles north of Baghdad.
A senior Iraqi military commander has said it will take a few days to fully dislodge al Qaeda-linked fighters from two key western cities.
Lt Gen Rasheed Fleih, who leads the Anbar Military Command, told state television that two to three days are needed to push the militants out of Fallujah and parts of Ramadi.
Pro-government Sunni tribes are leading the operations while the army is offering aerial cover and logistics on the ground.
Fighting has raged in Iraq's western Anbar province since last Monday, with troops from the Islamic State in Iraq and the Levant taking over the centre of Fallujah and some parts of Ramadi.
Residents say it has been quiet in Fallujah since Saturday night, while sporadic clashes took place in Ramadi.
US Secretary of State John Kerry has said America will support Iraq in its battle against the militants but said the US would not send troops to Iraq, calling the battle "their fight".
Mr Kerry made the comments as he left Jerusalem for Jordan and Saudi Arabia to discuss his effort to broker peace between Israel and the Palestinians.
He told reporters the US was very concerned by the al Qaeda-linked gunmen's successes in Fallujah and Ramadi.
Anbar province is a vast desert area on the borders with Syria and Jordan. It was the heartland of the Sunni insurgency that rose up against American troops and the Iraqi government after the 2003 US-led invasion that toppled Saddam Hussein.
Fallujah became notorious among Americans when insurgents in 2004 killed four American security contractors and hung their burned bodies from a bridge.
Ramadi and other cities have remained battlegrounds as sectarian bloodshed has mounted, with Shia militias killing Sunnis.
"We are very, very concerned about the efforts of al Qaeda and the Islamic State of Iraq in the Levant (ISIL), which is affiliated with al Qaeda, who are trying to assert their authority not just in Iraq, but in Syria," Mr Kerry said before leaving to visit Jordan's King Abdullah II and Saudi Arabia's King Abdullah.
"These are the most dangerous players in that region. Their barbarism against the civilians in Ramadi and Fallujah and against Iraqi security forces is on display for everyone in the world to see."
Meanwhile, Syrian rebels have seized a compound held by al Qaeda-linked fighters in a northern town, amid some of the most serious infighting between rebels battling president Bashar Assad. The Britain-based Syrian Observatory for Human Rights said that the rebels seized the compound in Manbij belonging to ISIL.