For an overall history of the war the best one IMO is probably going to be (since it's not finished yet) Allan R Millett's. So far he's written volumes on 1945-50 and 1950-51 ("The War for Korea", "A House Burning" and "They Came from the North" respectively). Millett's view of the war as really having started in the late '40's is spot on IMO, and that first book is a must to understand the war IMO, whatever books one reads about the conventional phase from June 1950.
For (mainly) US Army ground operations the official history is prety good, especially the first volume Appleman's "South to the Naktong, North to the Yalu", a very good book by any standard of military history.
Many of the tomes by well known American authors (Halberstam, Fehrenbach, Clay Blair, etc.) are IMO pretty much derivative of the official history and only add a bit more 'color' from the front lines but often a lot of the author's own opinions. The first can be valuable, but the latter usually isn't, to me. I don't think any of those books overall are better than the official history, especially not Appleman, and don't match Millet.
Another book on a portion of land campaign, the early fighting and Pusan Perimeter campaign which is really outstanding is "Fighting on the Brink" by Uzal Ent. Ent was a junior officer in the 27th Infantry at the time, but writes 99% as historian rather than participant. However he interviewed a large number of other participants and reconstructs battles in minute detail. It's another excellent book for any military history, IMO. *He* credibly challenges Appleman on some points, not just assuming the 'official history must be putting the US Army in a too favorable light' or is otherwise wrong because *some* participant (including ones interviewed by Appleman) didn't happen to agree with what Appleman decided on as the most likely truth. Ent really builds evidence bottom up where he disagrees with Appleman.
Another junior officer in 27th Infantry, Addison Terry, wrote "Battle for Pusan". This is strictly a first hand memoir but Terry was in the thick of it, and wrote with great humor, so it's exceptionally entertaining.
On a really forgotten part of 'the forgotten war', from US perspective, the ROKA's updated official history of the late 1990's is also pretty interesting, and the English version is free online (see link). This is also a pretty straight book for an official history (a previous version from much earlier was pretty propagandistic). It's remarkable from reading it how well the ROKA often fought, especially against the North Koreans (they had a mental block about the Chinese which lasted to some degree for the rest of the war) compared to some American lore, but it's basically corroborated in Appleman's limited ROKA coverage for the early period, and Ent felt the ROKA fought harder than his own Army.
('The Korean War' about 1/3 way down the page)
Robert Heinl's "Victory at High Tide" about Inchon is somewhat of a work of Marine Literature rather than a true history book (all Marines are heroes, none were unready for war, their leaders didn't make mistakes which got people killed, though Army leaders of course did, etc), but it's hard to put down, it's so well written.
Edited by JOE BRENNAN, 19 January 2011 - 2117 PM.