One car bomb attack killed at least five people in central Baghdad. Another in a road tunnel in Karrada district killed at least three.
Later seven people, including women and children, died as four mortar bombs hit a south Baghdad residential district.
The attacks came as the authorities continued a major security push.
US President George W Bush said it might take months for the operation to show results.
"If American forces were to step back from Baghdad before it is more secure, a contagion of violence could spill out across the entire country," he said in a statement to mark the anniversary.
More than 50 people were injured in Tuesday's attacks.
In a fourth incident, a car bomb exploded in a car parts market in south Baghdad, killing one person.
US and Iraqi troops are patrolling Baghdad to curb insurgent and sectarian violence that has claimed tens of thousands of lives since 2003.
There were no deadly bombings in the capital on Monday, but police said they found the bodies of 30 people who had been shot in various parts of the city.
Chemical bombs
Also on Tuesday, US officials said seven people suspected of procuring chemicals for bomb attacks and having links with Al-Qaeda have been detained by the United States military in the northern Iraqi city of Mosul.
The raids come three days after eight people died in a gas attack in Falluja, the fifth such attack in Iraq this year.
Earlier on Tuesday, the British military handed over a key base in the city of Basra to local Iraqi forces.
The handover of the base, which has served as a headquarters for British troops in the city for the last four years, comes four weeks after Tony Blair said the number of British troops in southern Iraq would be reduced by 1,500.
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~00~RS~)