Honestly, you almost can't go wrong. I used to just go to the bookstore and pick up any WWII memoirs or first person accounts I could find and I was never really disappointed.

Other than soldiers from the Band of Brothers or other Authors more well known; one book did occur to me: The Bridge at Remagen by Ken Hechler but I think that was because it involves a specific important event of the war. A lot of the books I read didn't, if I recall correctly, involve landmark battles or events necessarily, but they were always tremendous reads

Nearly every entry at http://ww2today.com/ includes an excerpt from a GI memoir or diary.

The site has descriptions of several recently published memoirs, as well as links to pages have digitized copies of otherwise unpublished diaries.

I'm not sure whether or not it's quite what personally you want in a memoir, but I'd highly recommend Studs Terkel's "The 'Good' War: An Oral History of World War Two" (note that the word good is in quotes in the title). As the sub-title says, it's an oral history that consists of many personal stories about what it was like during the war. Most of those stories are from military personnel, mostly American, but there are also stories from people on the home front and whatnot. All-in-all it gives you a good idea of what it was like to live during the war.

One of the stories that struck me (caution: it's been a long time since I read it), is of a US marine during a lull in combat on a Pacific island, watching another marine casually flipping pebbles into an upturned skull. The chilling part is that he realized the other guy wasn't doing it to be macabre or vindictive - he was just bored and the skull was lying around.