Mark Gruenwald wrote a Captain America story where Cap was forced, to save lives, to kill an Ultimatum soldier. Cap stated afterward that he had never killed anyone before, not even during the war.
I've seen that statement roundly criticized or dismissed a fair number of times*. Fans think it's unrealistic, or doesn't fit since Cap was a soldier during the war. I'm pretty sure Brubaker's either shown Cap killing during the war in flashback, or alluded to it. Also, I think it contradicts what was depicted in Captain America comics from World War 2.
I see people's points about it being silly to say Captain America never killed anyone, not even in the middle of a war. No one (that I've seen) is arguing he'd enjoy killing, only that he'd do it if the situation required it. Still, I never really had a problem with the idea that he hadn't killed. When I would have first read those comics, it was because he was a superhero, and they don't kill, and so he wouldn't kill anyone, even in war. When I was a bit older, I probably figured he was too lame to kill anyone. That's for cooler, hardcore characters**.
Nowadays, I'm closer to how I thought in the beginning, but it's not that he wouldn't as much as he doesn't need to. He's Captain America, he has physical gifts and training the average soldier didn't have. Situations where they have to kill or they'll die themselves (or secondarily, the mission fails), he can get through non-lethally because of his advantages. He could knock those Nazis out and take them prisoner. It's war, he's allowed to take prisoners. I can picture that in the Marvel Universe there were a lot more captured Axis soldiers, and fewer dead ones, than in our actual history.
* Brian Cronin had it as one of his 5 most ridiculous moments from that stretch of Gruenwald's Cap run, and the commenters seemed to agree with him.
** That may be overstating it. Even in the '90s I wasn't a huge Punisher or Ghost Rider fan. But I didn't have a high opinion of Cap, who I thought spent too much time making inspirational speeches and ordering people around.