The last I heard, more than 4000 US soldiers have died in Iraq, plus who knows how many soldiers from other countries, not the least of which is Iraq itself.
I would say about 5000, since 2003. Plus maybe 500 (notice I didnt say plus or minus). For a "war" that number is not too bad compared to what the outcome of other wars is.
As of the date of this answer, there have been 4694 Iraqi Coalition casualties incurred thus far during Operation Iraqi freedom, 4378 of which were American.