Okay, well that includes countries such as Spain and the Dominican Republic. I found this:
United Kingdom: 9,000 soldiers
Italy: 3,000 soldiers, some serving as police and engineers
Poland: 2,400 soldiers
Ukraine: 1,600 soldiers
Netherlands: 1,100 soldiers plus a logistics team, a field hospital, military police and 200 engineers
Japan: 1,100 soldiers assigned to reconstruction
Australia: 800 soldiers
Romania: 700 soldiers plus 149 de-mining specialists, military police and "special intelligence" members
South Korea: 600 military engineers and medics
Bulgaria: 480 soldiers plus chemical warfare experts
Thailand: 440 soldiers assigned to humanitarian missions
Denmark: 420 soldiers including medics and military police
El Salvador: 360 soldiers
Hungary: 300 soldiers
Norway: 179 soldiers, mostly engineers and mine clearers
Mongolia: 160 soldiers involved in peacekeeping
Azerbaijan: 150 soldiers taking part in law enforcement and protection of historic monuments
Portugal: 125 soldiers functioning as police officers
Latvia: 120 soldiers
Lithuania: 115 soldiers
Slovakia: 102 soldiers
Czech Republic: 80 soldiers, serving as police
Philippines: 80 soldiers plus police and medics
Albania: 70 non-combat troops
Georgia: 70 soldiers
New Zealand: 60 army engineers assigned to reconstruction (expected to leave in Sept. 2004)
Moldova: 50 soldiers including de-mining specialists and medics
Macedonia: 35 soldiers
Estonia: 30 soldiers
Kazakhstan: 30 soldiers (expected to leave end of May 2004)
Source:
http://www.cbc.ca/news/background/iraq/foreigntroops.html