Now that the wars in Iraq and Afghanistan have been simmering for a number of years, there are several good books written about combat in these theaters. I'll put aside books about the politics of the war or grand strategy. These three are mainly about combat and the lives of the soldiers risking their lives for a greater goal in the Middle East and Central Asia (in the order I read them):
The Long Road Home:
This one is an account of a major battle between the US Army and Mahdi militiamen in 2004. Written by Martha Raddatz, it is similar in style and story to Black Hawk Down. It is a detailed account of the battle, the soldiers, and their families. I read this one quite a while ago, so my memory of it isn't the best, but it was an excellent account of the beginning of the insurgency in Iraq.
Written by Paul Rieckhoff, an Amherst graduate and current chairman of the IAVA, this is a gritty look at combat and life in a small combat outpost. His unit entered Iraq shortly after the invasion proper ended and Iraq had been "liberated". The book is a great look at the day to day grind of a small unit in Baghdad. The book is at times hilarious, highly critical, deeply sad, and ultimately very real. At times it feels more like Catch-22, other times Platoon. Rieckhoff makes no effort to hide his feeling about the war itself and how it was and is being waged. He is very critical of the lack of equipment and training given to his unit before deployment, as well as the war in Iraq in general.
This book, just recently released, is written by Donovan Campbell, a guy who graduated from Princeton, but enrolled in OCS instead of heading off to a cushy investment banking job. He served two tours in Iraq as a Marine. The first was as an intelligence officer, the second as a platoon leader in the capital of Anbar Province, Ramadi. Fallujah got most of the press, but Ramadi was a very violent city, and Campbell's unit sustained the highest rate of casualties of any unit since Vietnam. Campbell pulls no punches in his description of combat and life in Ramadi. He certainly doesn't shy away from describing his own weaknesses as a leader, or the idiosyncrasies of war. He does a masterful job of illustrating the bond formed between his men over their time in Iraq. The full title calls it a "Story of Courage, Leadership, and Brotherhood", but Entertainment Weekly's review put it better, saying "Joker One isn't as much a story of war as it is a story of love." The book makes no political points, it is merely a very moving account of young men in a very tough situation.
For more immediate reading about the men and women serving their country in Iraq and Afghanistan, Gary Trudeau put together The Sandbox, a compilation of blogs by military folks stationed in Iraq and Afghanistan right now.