In the Spock-heavy "City on the Edge of Forever" (the only episode I can name), Spock correctly convinces Kirk that there are trade-offs and you can't get everything you want. Also, I think Kirk makes Spock work harder by appealing to his emotions.
shamelessly I once tried to steelman Spock in 'City', and the result was a fic 'Thinking like demented you' on ff.net (hides under the table)
City On The Edge Of Forever: Spock uses primitive technology to construct a machine to access the information stored in his tricorder. Genius is genius regardless of surroundings...
The Empath: Spock has the flash of insight that his own resistance to the energy field is what is empowering it.
The Galileo Seven: When all hope is lost Spock chooses to bet all on a desperate act, he jettisons all the remaining fuel to signal the Enterprise, knowing having done so within seconds the shuttlecraft will spiral into the atmosphere and burn up
In Galileo Seven Spock also says something like, "I, for one, do not believe in angels," indicating his skepticism about an afterlife. Does that make Spock the first (implicitly) atheistic character on a network TV series?
Beats me. I'd guess Twilight Zone, Outer Limits, Dr. Who or some other show snuck the concept in somewhere.
The Twilight Zone has more of a religious look-and-feel to it, with allusions to biblical stories and folk christian beliefs. One episode even features a christian martyrdom without once mentioning Jesus.
It's not TOS exactly, but I always liked his character arc in the movies. It was the only good part of 1 and 5.
I don't consider him a rationalist character. He is always hung up about what is logical, as opposed to what is observably right.
Uhura: Mr. Spock, sometimes I think if I hear that word "frequency" again, I'll cry.
Spock: It is illogical for a communications officer to resent the word "frequency."
What kind of answer is that? "Too bad you dislike your job?" A rationalist answer would have been something along the lines of "Can you explain why, maybe we can find out what went wrong with your feelings and find a way to fix them or work them around?"
There is a difference between rationality and smartassery.
Hence "(straw)" in the title. See e.g. this summary of a talk by Julia Galef about the difference between being a Straw Vulcan (memetic hazard warning: TVTropes) and being an actual practitioner of rationality.
[EDITED to link to the LW article that has a transcript of the original talk an a link to the YouTube video.]
I, Mudd:
Logic is a little tweeting bird chirping in a meadow. Logic is a wreath of pretty flowers which smell BAD.
Hopefully at least one or two would show a virtue of non-straw rationality.
Episode list