It's not flashy, but I think Waltz is my favorite Deep Space Nine episode.
http://memory-alpha.wikia.com/wiki/Waltz_(episode)
The progression from showing Dukat sympathetically as misunderstood gradually creeping towards a Master Race maniac, along with Sisko's realization of what's really going on gives me the chills. No glitz or fancy special effects needed, just airtight writing backed up by excellent acting and direction.
I guess I ought to post a personal favorite for each series. For the Next Generation it's easy: Darmok
http://memory-alpha.wikia.com/wiki/Darmok_(episode)
There's a lot to like here, but the reason it stands out to me is because it asks a simple question that hardly any other episode does: "What if aliens actually thought in a way that was foreign to us, how would we struggle to understand them?" Echoes of Stanisław Lem's Solaris.
It rarely gets mentioned on the "best of" lists, but Enterprise's episode Carbon Creek is my favorite.
http://memory-alpha.wikia.com/wiki/Carbon_Creek_(episode)
It has a lot of the things that make City on the Edge of Forever so memorable, (the clothes-stealing scene was a nice homage) but it focuses more on the the Vulcans' efforts at fitting in and coming to appreciate the culture they find themselves in. Stories of learning to come to a greater understanding of others is where Trek shines.
My knowledge of Voyager is more scant, but the one I enjoyed most was Message in a Bottle.
http://memory-alpha.wikia.com/wiki/Message_in_a_Bottle_(episode)
My favorite thing about Voyager has always been the doctor. Seeing him get a chance to defeat the Romulan plot through his own subterfuge is just a whole lot of fun.
As a programmer I especially enjoyed the scene where Paris and Kim attempt to program a replacement doctor (how hard can it be?) only to have it stuck reciting Grey's Anatomy from the beginning.
I haven't finished the Animated Series yet, and I'll give Discovery a chance to at least finish season 1 before deciding on a favorite, though I doubt I'll like another episode as much as the pilot featuring Captain Georgiou.
@technomancy Sokath, his eyes open!
Though you did not include your favorite from Star Trek: Orville.
For the original series it's City on the Edge of Forever.
http://memory-alpha.wikia.com/wiki/The_City_on_the_Edge_of_Forever_(episode)
A time travel adventure that takes the consequences seriously. Pathos with some fish-out-of-water comedic elements. Maybe a bit clunky by modern standards, but an indisputable classic that still holds charm.
#startrek #tos