I enjoyed Robert Graves Goodbye to All That (WW1)

I am surprised that All Quiet on the Western Front (Im Westen nichts Neues) by Erich Maria Remarque hasn't been mentioned yet. Sure, it's a novel, but it is written by a veteran and based on his own experiences. The Nazi's hated the book, so that alone should be recommendation enough.

Concerning the Second World War I can highly recommend Panzer Commander by Col. Hans von Luck. As a company (later regiment) commander he saw action on almost all German fronts: France, the USSR, North Africa and France again. He's no foot soldier, but it's still very much a soldier's account of the Second World War from a German perspective. He also describes the years he spent in a Soviet prison camp after the war.

Storm of Steel by Ernst Junger is his first hand account from WW1. There are many, many, first-hand accounts of WW2, the best in my opinion is "The Forgotten Soldier" by Guy Sajer.

Not sure if it's entirely what you're looking for but here's a pretty good c-span panel featuring Babe Heffron and some of the guys Band of Brothers was based on.

If you're looking for solely combat/"day in the life" information on the German side of WWII in the East then I suggest:

*In Deadly Combat by Gottlob Bidermann

*Blood Red Snow by Gunter Koschorrek

*Black Edelweiss by Johann Voss

However, these gloss over or minimize the Ostheer's crimes in the East, as do most German diaries and memoirs (Secondary sources are better). For a couple that offer a clearer picture of the German mindset during this era:

*Eastern Inferno by Christine Alexander and Mason Kunze

*A Mind in Prison by Bruno Manz

For the Red Army accounts tend to be more balanced (Candid discussion of war crimes):

*A Writer at War By Vasily Grossman (Cannot recommend this one more)

*Victims, Victors by Roman Kravchenko-Berezhnoy (Also excellent)

*Through the Maelstorm by Boris Gorbachevsky

*Red Road from Stalingrad by Mansur Abdulin

The Good War by Studs Terkel is pretty great.

Britain's Last Tommies by Richard Van Emden records the memories of several ex-soldiers. I forget what other books of his I've read, but I recommend him for his interview-type books such as this, there's at least another I've read. EDIT: Forgot to mention the soldiers were Great War combatants.

Try Forgotten Voices of the Great War.

Mammoth Book of Eyewitness: World War I. Very good compilation of letters bome and diary entries from all sorts of people. Ex: British infantry at Ypres, a sailor at Jutland, a sniper at Gallipoli, the Red Baron strafing Russian infantry, a journalist... very good.