The theme of "sacrifice" is an important one in the movie. In war, sacrifice is something a soldier is implied to be able to do at a moment's notice. In Saving Private Ryan, it is the sacrifice of a squad of soldiers for one soldier. The squad spends the majority of the movie tyring to find one young soldier because his family has sacrificed enough for the cause during WWII. Many of the squad are sacrificed in order to find Ryan, and at the end, a captain is sacrificed for a private.
"Self worth" is another theme. What Captain Miller says to Ryan at the end, "James, earn this...earn it," caps the end of the movie where the older Ryan tells his wife, "Tell me I'm a good man." For over forty years, Ryan has been living with the question of whether or not he has earned the sacrifice of those men.