The blasts targeted residential buildings in a mix of Sunni and Shia areas of Baghdad on Tuesday morning.
Police said two car bombs were detonated in Bajkouk, Khadamiya district, killing at least five people.
In Baghad's western Shula district, another car bomb exploded, causing some buildings to collapse. Several people died in the explosion, Iraqi security sources said.
Al Jazeera's Zeina Khodr, reporting from Baghdad, said those attacks occurred in residential neighbourhoods of the capital.
"[Shula] is a mostly Shia neighbourhood. It used to be a former stronghold of the Mahdi Army, the armed wing of the Sadr movement," our correspondent said, referring to supporters of Moqtada al-Sadr, a Shia leader.
Shula has been a relatively quiet neighbourhood, having not seen been the target of attacks in recent months.
Police said another of the blasts was carried out by a suicide bomber, who detonated explosives on Haifa street in the central Salhiya neighbourhood, near the national museum.
Our correspondent said it was not yet clear what the target of that attack was.
"We're getting conflicting reports on the target. Some reports say it was the public works ministry, other reports say he [attacker] blew himself up outside a popular restaurant," she said.
Al Jazeera has also received reports that a suicide bomber attacked a police station in southern Baghdad's al-Amel district, although it was not yet confirmed.
Political unrest
Tuesday's co-ordinated strike follow similar attacks just two days earlier. On Sunday, three suicide car bombsnear foreign diplomatic missions killed at least 30 people and wounded hundreds more.
In the past five days, four attacks have left more than 100 people dead.
The spate of violent attacks comes as Iraqi politicians continue wranglings to form a coalition government following last month's general elections. No clear winner emerged from the March 7 poll.
The Sadr political bloc was expected to announce who it would back for prime minister on Tuesday after holding an unofficial referrendum among its supporters, but said late on Monday night that the decision was being postponed.
Nouri al-Maliki, the incumbent prime minister, is reported to have met the group last night, but no details of any agreement have emerged. The Sadr bloc has in past indicated it would not support al-Maliki staying on for another term as prime minister.
Our correspondent in Baghdad said a lot of negotiations are taking place, but "no agreements so far, no progress, and there is a real fear that the security situation will deteriorate".
"Over the past few days we've been seeing car bombings, shootings, mortar round being fired, as well as improvised explosive device attacks".
