The vast majority of countries that participated in OIF have withdrawn their forces. The UN mandate legalizing the presence of foreign soldiers in Iraq expired at the end of 2008. The Iraqi cabinet approved a security pact with the US. Read the text of the agreement here. The Iraqi cabinet drafted a law permitting the presence of soldiers from specific countries.
In its Iraq Weekly Status Report of 12/10/2008 the State Department listed 16 non-US countries in support Operation Iraqi Freedom by contributing a total of about 6,350 personnel in Iraq. In the report of 12/31/2008 (found here), the State Department noted on slide 27 that "the UN-mandated coalition will cease to exist" as of December 31,2008.
On its website MNF-I (4/30/09) lists 3 non-US countries as coalition partners - Australia, Romania, and the United Kingdom.
For coalition casualties, please refer to icasualties.org.
There are multiple unofficial sources that have kept track of Coalition forces.
Some of the best that I have found, and in some cases worked on, are here:
Iraq Index from The Brookings Institution Updated weekly
Multinational Force In Iraq from Wikipedia Updated continuously
CRS Report RL32105 from US Embassy in Italy 26 DEC 2007
Iraq Weekly Status Report Updated weekly (no longer maintains a list)
GlobalSecurity.org's Iraq Coalition Page 3 SEP 2007
Official MNF-I Coalition Partners Website 17 OCT 2008
Centcom Coalition Countries Undated
Australia withdrew all of its MNF-I forces in July 2009.
El Salvador, Estonia, Romania all withdrew their forces in early 2009.
Ukraine, Albania, Moldova, and Bulgaria all completed their Iraq missions and began withdrawing soldiers in mid-December.
According to the New York Times, Tonga's military contingent withdrew in December.
According to the Times of London, Macedonia and Bosnia & Herzegovina ended their Iraq commitment in late November 2008.
Azerbaijan announced that it will withdraw its soldiers from Iraq by the end of the year. On December 3, VOA News confirmed that the Azerbaijani troops ended their mission.
Romania announced that it will withdraw its soldiers by the end of the year but that it may maintain some military personnel in Iraq as part of an as yet undefined mission.
Latvia withdrew its three soldiers from Iraq in November 2008.
Poland withdrew its soldiers in October 2008, according to the New York Times.
Kazakhstan withdrew its troops in early October 2008, according to MNF-I.
Armenia withdrew its contingent in October 2008, according to AFP.
Mongolia withdrew its combat troops in mid-September.
It appears likely that the Czech Republic withdrew its contingent that was part of MNF-I and that it currently only maintains a contingent in Iraq as part of the Nato training mission. This appears to be the case according to the website of the Czech Republic Ministry of Defense.
Because of the conflict with Russia, Georgia withdrew its soldiers from Iraq in August 2008. The United States airlifted Georgia's soldiers out of the country, despite a Russian protest.
The Lithuanian Ministry of National Defence reported that Lithuania withdrew its contingent of soldiers in July 2008.
It appears likely that Singapore ended its ground commitment to OIF. MNF-I and the State Department no longer list Singapore as a country contibuting to OIF. However, they do still maintain a tanker off the coast of Iraq. Read about that naval commitment here.
The Australian Ministry of Defense reported that the Overwatch Battle Group-West and Australian Army Training Team-Iraq contingents had left Iraq. Australia still maintains a ground force of some 350 personnel within Iraq and therefore this website will continue to monitor their contribution.
It appears almost certain that Denmark's forces no longer participate in OIF but rather condcut training missions under the auspices of NATO. According to the Danish Foreign Policy Yearbook, Denmark withdrew its troops under MNF-I in the summer of 2007.
Voice of America reported that Japanese ground forces withdrew from Iraq in June 2006. However, Japan continues to airlift materials and personnel between Iraq and Kuwait. The Japanese Self Defense Forces keep track of those resupply missions here.
The Guardian, CRS, and The Brookings Institution reported that Italy had ended its troop commitment to MNF-I as of December 2006.
The AP reported that Lithuania withdrew its troop contingent in August 2007. However, it recently came to my attention that Lithuania redeployed its forces in October 2007 and currently maintains a force in Iraq under MND-CS.
Xinhua reported that Slovakia withdrew the last of its soldiers from Iraq in December 2007.
Updated information on each country that currently maintains forces in Iraq as part of Operation Iraqi Freedom.
100 personnel protect the Australian embassy in Baghdad as part of Operation Kruger