The attacks, which left nearly 70 others wounded, primarily targeted marketplaces that are often crowded on Fridays, the weekly holiday in Iraq, and took the death toll from a week of violence to more than 100.
Twin explosions that struck at a bird market in the north Baghdad neighbourhood of Kadhimiyah, site of the shrine of a revered figure in Shii'te Islam, killed at least 16 people and wounded 43 others, security and medical officials said.
The two car bombs were set off just after 9:00 in the market, which is typically packed with people on a Friday.
Militants have targeted Baghdad's crowded bird markets in the past.
On 1 February 2008 - also a Friday - 100 people were killed by two explosions in such markets in central and east Baghdad.
The explosives were strapped to two mentally impaired women and then triggered by remote control in co-ordinated blasts, a top Iraqi security official said at the time.
And in the predominantly-Shi'ite Iraqi province of Babil on Friday, two car bombs in the town of Shomali, south of Baghdad, killed 13 people and wounded 47 others, according to security and medical officials.
The first explosion went off on the town's outskirts, while the second was detonated in a market.
Women and children were among the casualties in both attacks, medics said.
Sunni militants, including al-Qaeda's front group in Iraq, often target Shiite neighbourhoods with deadly attacks in a bid to push the country back to the sectarian bloodshed that blighted it from 2005 to 2008.
The violence is the latest in a spike in unrest in Iraq, which has been struck by waves of car bombs and suicide attacks amid a political crisis and weeks of rallies in Sunni-majority areas calling for the ouster of Shiite Prime Minister Nuri al-Maliki.
Renewed demonstrations took place on Friday in Sunni areas of Baghdad, as well as the northern and western cities of Mosul, Samarra and Ramadi.
The protests have largely railed against alleged targeting of minority Sunnis by the Shiite-led authorities, but have more recently focused on demands for the resignation of the premier.
A total of 102 people have been killed in violence nationwide in the past week, and January was the deadliest month in Iraq since September according to an AFP tally.
Among the attacks since Saturday was a string of three suicide bombings in as many days.
The violence comes with less than three months to go before provincial polls in April, Iraq's first vote since March 2010 and a barometer to gauge the popularity of Maliki and his opponents.