The Iraq War costs for the U.S. have been estimated at between $8.2 million and $12.3 million per hour by the Congressional Budget Office.
A succinct explanation of the CBO reports can be found at About.com: http://usgovinfo.about.com/library/weekly/aairaqwarcost.htm [1].
The site provides estimated monthly costs, proportedly from CBO reports. I figured the hourly costs by dividing the $6 billion to $9 billion monthly costs by 30.4375 days in a month, and then divided that answer by 24 hours in a day.
If the U.S. spends $6 billion a month conducting the war in Iraq, the hourly cost would be roughly $8.2 million. At the high end, it costs $12.3 million.
Many other costs are not included in these figures.
For more information, you might want to follow this story: http://www.tpmcafe.com/story/2006/1/5/11510/30624 [2].