The unrest comes amid a political crisis that has pitted Prime Minister Nuri al-Maliki against several of his erstwhile government partners and with more than four weeks of anti-government protests in Sunni majority areas hardening opposition against the Shiite leader's rule.
Tuesday's blasts struck an army checkpoint south of Baghdad, a military base north of the capital, and a mostly Shiite neighbourhood in the city's north, security and medical officials said.
No group claimed responsibility, but Sunni militants often launch attacks in a bid to destabilise the government and push Iraq back towards the sectarian violence that blighted it from 2005 to 2008.
"One of my friends was hurt in his head, and another was seriously wounded in his chest," said 41-year-old mechanic Ali Jassim at the site of the Baghdad blast, before angrily shouting: "The politicians are busy with keeping their posts, and we are suffering from these explosions!"
In the attack, six people were killed when a car bomb was detonated near an army camp in the town of Taji, 25 kilometres (15 miles) north of Baghdad, an army officer and a medical official said.
At least 20 other people were wounded.
South of the capital in the town of Mahmudiyah, at least five people were killed and 14 wounded by a suicide car bomb, officials said.
Mahmudiyah lies within a confessionally mixed region known as the "Triangle of Death" because of the frequency of attacks during the worst of Iraq's insurgency in the wake of the 2003 US-led invasion.
A car bomb near a market in the north Baghdad neighbourhood of Shuala killed five people and wounded 12, while gunmen killed five officials who were transporting salaries between oil refineries near the town of Baiji.
Pieces of metal were littered across the scene of the Baghdad attack, with several cars badly damaged or completely burned, an AFP journalist said.
The insurgents who carried out the latter attack fled, and the funds were recovered, officials said.
Meanwhile, eight different shootings and bombings in Diyala, Nineveh and Salaheddin provinces north of Baghdad killed five people and wounded 12 others.
The violence broke four days of relative calm in Iraq following a spate of attacks claimed by Al-Qaeda's front group that killed at least 88 people on January 15-17, according to an AFP tally.
The militant group is widely seen as weaker than during the peak of Iraq's sectarian bloodshed, but is still capable of carrying out mass-casualty attacks on a regular basis.
The latest wave of violence meant the overall death toll from bloodshed in Iraq this month has already surpassed that of any of the previous three months, according to an AFP tally based on reports from security and medical officials.
Iraq's political crisis has pitted Maliki against several of his ministers who have accused him of authoritarianism and sectarianism just months ahead of provincial elections.
Weeks of anti-government rallies in Sunni Arab majority areas, supported by parties that are members of Maliki's unity cabinet, have increasingly called for the premier to quit.
The violence and political troubles come three months before provincial elections, Iraq's first polls in three years and a key barometer to gauge the popularity of Maliki and his rivals.
Attacks in Iraq are down from their peak in 2006-2007, but they are still common across the country.