What is the current troop strength of U.S. forces in Iraq?
Another one of the fine librarians here at radref was kind enough to provide us with some additional information to help answer this question. He suggested checking out Global Security for an article on Iraq and the Asian theatre of operations. There is an independent research consortium's website dedicated to the War in Iraq, Conflict in Iraq, where more information can be found. There's also a great resource on FedStats which provides information on troops by region. There's also some information linked within Radical Reference itself, which leads to a link to the ALA's International Responsibilities Task Force. I hope these additional resources are helpful.
According to an archived "Morning Edition" story on npr.org from 15 August 2005, there were 138,00 U.S. troops in Iraq at that point. To find more current information, I searched the online New York Times archive for "troop levels in Iraq" and "number of troops in Iraq" and found that it's a difficult number to pin down. As of 18 December 2005 (as reported in "Asking Patience, President Cites Progress in Iraq"), there were 160,000 U.S. troops in Iraq, a spike caused by the elections there. As of 31 January 2006 (in the article "Iraqi Official Says Foreign Forces Could Fall Below 100,000 This Year"), there were 140,000 U.S. troops in Iraq. Finally, on 3 February 2006, I found a story ("$120 Billion More is Sought for Military in War Zones") that reports that there are 130,000 U.S. troops in Iraq.
In short, currently, there are currently anywhere between 130,000 and 140,000 U.S. troops in Iraq.