according to CNN it's 906 as of 7/23/04
http://www.cnn.com/SPECIALS/2003/iraq/forces/casualties/There have been 1,027 coalition deaths, 906 Americans, 61 Britons, six Bulgarians, one Dane, one Dutch, one Estonian, one Hungarian, 19 Italians, one Latvian, six Poles, one Salvadoran, three Slovaks, 11 Spaniards, two Thai and seven Ukrainians, in the war in Iraq as of July 23, 2004 (Graphical breakdown of casualties). The list below is the names of the soldiers, Marines, airmen, sailors and Coast Guardsmen whose families have been notified of their deaths by each country's government. At least 5,804 U.S. troops have been wounded in action, according to the Pentagon. The Pentagon does not report the number of non-hostile wounded. This list is updated regularly.