While I'm at it...
The flip side of the reading list below might be a compilation of books that an interested civilian would read in order to better understand the military. Charlie's graduate coursework included approximately nothing on the military itself (only the brilliant SWAMOS curriculum rescued her). Given the lack of day-to-day interaction between civilians and military personnel, most folks don't have the opportunity to listen to war stories over beer (for which there really is no substitute).
And imperfect, but not irrelevant, solution: reading the books the services say are important. This amounts to something of an anthropology exercise. Sometimes this information can be found on Commandant's and Chairman's reading lists. Other times, certain books just come to be revered by a service. (Unfortunately, Charlie's knowledge is rather narrowly limited to the Army and Marine Corps.)
The quintessential Army saga is Once an Eagle. Charlie realized she had to read this when she overheard someone referring to a third-party as "a real Courtney Massengale." Ouch.
The Marines are a little more self-conscious in their propa-- I mean, mythmaking. (Krulak's First to Fight is on the Commandant's reading list at every grade.) Two modern classics: Jim Webb's Fields of Fire and Stephen Pressfield's Gates of Fire. Charlie's personal favorite is Tom Ricks' Making the Corps (which she read after Nate Fick claimed he joined the Marines largely because of it.)
There's no substitute for the real thing, but sometimes books tell you things that soldiers and Marines won't.
Update: Charlie's favorite Army strategist writes in with two more suggestions for the Army list (which she can't believe she overlooked): Gen. Moore and Joe Galloway's We Were Soldiers Once...and Young and (of course) Michael Shaara's Killer Angels.