Does the OP (or anyone else) have any individual stories in mind that might have been forerunners of the Star Trek format?
No Contact comes immediately to mind - it's the one where a starship is going to try to penetrate the galactic barrier that has already claimed 5 ships. Meanwhile, an old crewmate of the captain's has stowed away aboard ship. A young up and coming officer has something to prove, for his father (also an old friend of the captain's) was lost on one of the lost ships. Off-duty, the captain and his confidante, the curmudgeonly ship's doctor, philosophize over the human condition and what the galactic barrier really represents.
Here's a great example:
Doc: What makes you think we can get through it?
Cap: Because we're ready for it. The others weren't. The entire hull is completely shielded with lead. We can crack through any radioactive cloud ever detected. Besides, we're equipped with some new UHF radio devices that should enable us to maintain radio contact with Earth. Nothing can happen, absolutely nothing!
Doc: Who are you trying to convince, Lewis?
Cap: Myself, I suppose. Smitty, five ships are missing, and men like Prentiss and Margudson and young Collier's father. I'm tired of seeing good men fed into that meat chopper.
Doc: Then why are we going?
Cap: We haven't any choice, Smitty. We're in a race. The kind of race where men and ships are expendable.
Doc: Well... at least it won't be boring. I'll have to play physician/morale builder and mother substitute for 112 slightly nervous men.
Cap: Heh. YOUR morale doesn't sound too good, Doctor.
Doc: As morale officer, I can state without fear of contradiction: it's terrible.
Maybe part of it is the delivery, but the episode really evokes both Star Trek pilots to me.
I recommend the version of No Contact on the first cd -- interestingly, they occasionally re-used scripts.