"A star captain's most solemn oath is that he will give his life, even his entire crew, rather than violate the Prime Directive."
(Kirk in "The Omega Glory")
I think that was pretty straightforward with little room to double-guess.
@ USS Triumphant
Interesting and believable scenario, however it has a touch of "everything is lost anyway so we can sacrifice our lives more easily".
What I found interesting in "Bread and Circuses" is that Scotty got a clear order but found an interesting way to do something about the situation without violating the PD:
SCOTT: But they have used the code term Condition Green, which means they're in trouble. But it also prohibits my taking any action. (ends log entry) Mister Chekov, pinpoint power source locations. Type, power, load factors, and how much our beams will have to pull to overload them.
Something else I have somehow always interpreted as one of the few excuses to ignore the PD is Spock's observation of the Organians in "Errand of Mercy". While it appears that the PD is not an issue at times of war, I nevertheless couldn't help to feel that Spock's report was having a relief character (along the lines "Damn it, we have to violate the PD but fortunately find out that we aren't doing any damage"):
SPOCK: Captain, our information on these people and their culture was not correct. This is not a primitive society making progress toward mechanisation. They are totally stagnant. There is no evidence of any progress as far back as my tricorder can register.
KIRK: That doesn't seem likely.
SPOCK: Nevertheless, it is true. For tens of thousands of years, there has been absolutely no advancement, no significant change in their physical environment. This is a laboratory specimen of an arrested culture.
If Spock provided all or some of the exceptions where not to apply the Prime Directive, I'd guess there are more TOS examples that qualify than usually assumed.
To partially answer those good questions at the end of Warped9
's opening post, I'd say a lot would depend on any aliens' experience with a history like ours, i.e. are we still making (ethical) progress or have we become ourselves an "arrested culture"...?