There are more than 150,000 troops in Iraq. The vast majority are American, but other countries have sizeable contingents, and some have just a handful of troops.
But some nations may be reconsidering their position in the light of continuing attacks against the occupation forces, and a rash of hostage-taking.
Click on the countries below to see where they stand.
The US has around 135,000 troops in Iraq. Along with Iraqi security forces, they are responsible for all of the north and west of the country, and much of the centre, including Baghdad.
Troop deployments are down from a high of about 150,000 during the war.
The Pentagon planned to reduce the number of American troops to about 110,000 by mid-2004.
But with no end to violence on the ground, US generals have appealed for more troops - and the defence department has agreed to keep the level at about 130,000 over the short term.
The main flashpoints have been Falluja and other parts of the "Sunni triangle", where hundreds have been killed in clashes between US forces and insurgents.
The cost of the US military presence in Iraq is running at nearly $4bn per month.
Politically, the deaths of US personnel and the cost of the war, along with continuing chaos in Iraq, could be very damaging to President George W Bush in the run-up to the presidential election in November.
The UK has about 8,700 soldiers in Iraq, down from about 40,000 during the war. UK forces lead a multinational force in the far south of Iraq, where generally the lack of security has not been as severe as in Baghdad and to the north of the capital.
Other countries working with UK troops include Italy, the Netherlands, Denmark, Romania, the Czech Republic and New Zealand.
UK officials have said their troop commitments to Iraq are long term. Prime Minster Tony Blair strongly supports a British role in Iraqi reconstruction and peacekeeping.
Polish soldiers are commanding a 9,000-strong 21-nation force in the south-central region of Iraq - in a zone between the US and UK-led areas.
Poland is contributing about 2,400 troops to the force.
Poland, along with most of the former communist countries of central Europe and the Balkans, was a firm supporter of the US-led attack on Saddam Hussein's Iraq. And alone among continental European countries, Poland sent a small military contingent to fight there during the war.
Spain sent about 1,400 troops to Iraq but these have since been withdrawn by the new prime minister Jose Luis Rodriguez Zapatero.
Spain was a key supporter of the US-led invasion of Iraq, but did not contribute troops to the invasion itself.
There has been a hostile public reaction to Spain's involvement in Iraq, and many associated their government's stance with the Islamist bomb attacks on four trains in Madrid, which killed nearly 200 people in March 2004.
Immediately he was elected in March, Mr Zapatero promised to withdraw troops unless they were put under UN command by July.
The last Spanish soldiers left Iraq on 21 May 2004.
France strongly opposed military action in Iraq.
It has not ruled out sending peacekeeping forces at a later stage, but it first wants to see a swift handover of sovereignty to the Iraqi people and a much stronger role for the United Nations.
It advised all French citizens to leave Iraq after a spate of kidnap attacks against foreigners.
Germany has ruled out sending troops to Iraq, saying it does not have the capacity.
It already has 10,000 troops committed in peacekeeping operations around the world, and has pledged to expand its peacekeeping operations in Afghanistan, where it already has 1,800 troops.
Ukraine has contributed about 1,650 troops, putting it among the largest contributors of non-US forces. It is working under Polish command in south-central Iraq.
Bulgaria has sent a 485-member battalion, which serves alongside Ukrainian troops under Polish command in central Iraq.
There are about 3,000 Italians operating in southern Iraq in the UK-led multinational force.
On 12 November 2003, 19 Italian military and police personnel were killed in a suicide attack on Italian police headquarters in Nasiriya.
It was the single biggest loss of life for a member of the coalition since the start of the war in Iraq in March - and Italy's largest military losses to hostile action since World War II.
Despite a number of Italians being taken hostage in Iraq, Prime Minister Silvio Berlusconi said he remained committed to the operation.
Portugal sent 128 elite police officers to Iraq on the same day as the bombing of the Italian base station in Nasiriya.
The Portuguese national guards are part of a multinational force
under British command which is providing security in the south of
Russia has not ruled out sending peacekeepers to Iraq, but like France, it would want an appropriate UN Security Council resolution to be passed. Russia wants to see a much stronger role for the UN.
Russia had hundreds of civilians working in Iraq on reconstruction projects, but arranged for them to be brought home after a spate of kidnap attacks against foreigners.
In a major blow for the US, Turkey withdrew an offer to send up to 10,000 military personnel to Iraq.
The offer had been controversial - highly unpopular with Iraqis and the Turkish public.
Some members of Iraq's US-appointed Governing Council said they would not accept troops from any neighbouring state on its soil.
Turkey would have been the first mainly Muslim nation to send a sizeable force to Iraq.
More than 2,000 Australian troops fought alongside American and British troops in the campaign. That force has been scaled down to about 850-strong.
Prime Minister John Howard says they will remain there as long
as they are needed, despite escalating violence.
But opposition Labor Party leader Mark Latham has promised to withdraw
the troops if his party wins elections expected later this year.
Japan has 550 troops in the country, engaged in a reconstruction and humanitarian mission in Samawa, southern Iraq.
Japanese Prime Minister Junichiro Koizumi came under enormous pressure to pull the troops out when Japanese hostages were kidnapped in Iraq.
But despite huge protests in his country over the country's largest foreign military mission since the Second World War, he vowed not to give in to "despicable acts".
South Korea has said it will send 3,600 troops to Iraq, to help in post-war rebuilding efforts.
Foreign Minister Ban Ki-moon said it had no intention of taking over
more-aggressive duties, despite initial requests from the United States.
The Philippines has nearly 100 soldiers in Iraq, and has also sent policemen and social and health workers. They are based in the south-central zone administered by Polish forces.
The Philippines Government is a key US ally and was among the first to commit troops, but President Gloria Macapagal Arroyo said mounting violence had led her to consider withdrawal.
About 440 Thai troops are stationed in the central Iraqi city of
Karbala, carrying out humanitarian and reconstruction work.
Bangladesh may contribute peacekeeping troops at a later stage - but only under the flag of the United Nations.
Bangladesh has vast experience of peacekeeping and uses such missions to promote its image abroad. It is committing troops in Liberia and in the Democratic Republic of Congo.
Pakistan would be likely to contribute troops to a multinational peacekeeping force, but only if it was led by the United Nations rather than the US.
India has said it would consider deploying troops only if there was an explicit UN mandate.