Some favorite subtle moments off the top of my head:
-The end of "City on the Edge of Forever", where Kirk doesn't say anything after he stops McCoy from saving Edith Keeler -- Everything Kirk is feeling is written on Shatner's face. And then that thousand yard stare Kirk has when they return to their own time, followed by, "Let's get the hell out of here." Classic.
-In "The Trouble With Tribbles," I love how the Klingon Korax apes Scotty's accent when he says, "Yer'right. I SHOULD." David Gerrold loved that moment, too.
-I love the little knowing glance that Sulu & Chekov share when Kirk brings up "Corbomite" at the end of "The Deadly Years."
-I love the moment in "Mirror, Mirror" where Scotty grabs Kirk's arm and says, "Jim!" as Kirk volunteers to stay in the Mirror Universe. Kirk just quietly says, "That's an order, Scotty" and that's the end of it. I believe that this is the only time that Scotty ever calls Kirk by his first name, and it's gold.
-I like the brief look of dismay that Kirk has at the beginning of TWOK when Spock asks him where he's going, before resignedly saying, "Home" with a half-hearted smile. Nice bit of acting by Shatner there, and it's our first glimpse as to just how unhappy Kirk is with his life. He hates that he has nothing else to do with his day, and that there's no one waiting for him when he gets home. Shatner gave his best performances in Nick Meyer's movies.
-I like how gingerly everyone dances around Data's Tasha hologram in "The Measure of a Man."
-Picard's last line in "Cause and Effect" where Captain Morgan Bateson is stranded in the 24th Century: "Would you mind beaming over here? There's something that we need to discuss."
-Similarly, the "Oh, SHIT" look on Rasmussen's face when Picard tells him "Welcome to the 24th Century" just as he's being hauled off to prison in "A Matter of Time."
-And the moment in "Unification, Part I" where Picard coaxes a Klingon ship out of the High Command with just a few well-chosen words. One of my all-time favorite Picard moments.
-"The Visitor" - The look of heartbreak on Ben Sisko's face when he realizes how much of his life Jake has thrown away in the hopes of seeing his father again.