On the original Star Trek I liked the Mirror, Mirror.
On TNG I thought A Matter of Honor and Measure of a Man were good episodes
Wasn't a big fan of the other Star Treks but I did like Death Wish from Voyager.
TOS: "City on the Edge of Forever" is and always will be the standout episode for me, though I think it would be really interesting to see Harlan Ellison's original script on screen. "Balance of Terror," "The Trouble With Tribbles," and "A Private Little War" also stand out for me.
TNG: "The Best of Both Worlds," "The Inner Light," "The Measure of a Man," "Darmok," "All Good Things..." There really are too many TNG episodes that are sheer greatness. I even like "The Game," even though it's got the Wesley Crusher Marty Stu Effect going on.
The DS9 finale, "What You Leave Behind"... I'm not sure I would call it my favorite episode, but it always... ALWAYS has me sobbing by the end without fail. In fact, I'm tearing up right now just thinking about Odo and Kira's goodbye. "The Visitor" also tends to choke me up pretty well. "Duet" is the standout from the first season. I'm also very fond of "The Way of the Warrior" because I love Klingons, and Worf is pretty much my favorite Trek character from any series. Another one that really struck me is "Hard Time," where O'Brien serves an entire years-long prison term in a simulation that actually only takes a few minutes, but has huge psychological effect. For sheer fun, I'd also have to include "Trials and Tribble-ations" and "Take Me Out To The Holosuite."
I still haven't seen too much of Voyager. In the early seasons, we didn't get UPN at my house, and the later seasons diluted the Borg from creepy powerful to villain of the week. I do recall that "Year of Hell" stood out to me, and so did "Tuvix."
I saw even less of Enterprise than of Voyager, because of its generally sub-par nature. I did really enjoy "Through a Mirror, Darkly," however, especially the little touches, like re-working the credits to reflect the alternate history of the Mirror Universe.
For the movies, I'd have to go with II, VI, and First Contact as my top three, not necessarily in that order.
City on the Edge of Forever - For all the foofaraw between Roddenberry and Ellison, it's probably the best of TOS. The expression on Kirk's face as he keeps McCoy from rescuing Edith Keeler, all by itself, is priceless.
A Taste of Armageddon - I REALLY enjoy this story, especially the whole concept of a society so convinced that war is inevitable that they attempt to make it clean and painless ... and forget what war is or what can happen when a third party enters the equation.
Balance of Terror - I remember when I first saw this episode, thinking that it was the outer space equivalent of The Enemy Below, with Robert Mitchum and Kurt Jurgens. Always a favorite.
A Piece of the Action - The one thing TOS did better than any of its progeny is laugh at itself, and nowhere better than with Bella Oxmix and the Iotians. Certainly "The Trouble with Tribbles" is good at that. This is just as good.
The Enterprise Incident - Third year of TOS was pretty thin, but this one deserves a nod, if for no other reason than to give some kudos to its author, D. C. Fontana, who had to use her initials rather than her name (Dorothy) to keep her wonderfully skilled hand in the game.
I agree with the other comments I see here about "The Inner Light" and "Best of Both Worlds" as it comes to TNG, and I would throw in "Relics," if only because of my fondness for James Doohan (I AM an engineer, after all!). The story arc of the Cardassian war on DS9 was where it truly came into its own in my mind, though the introduction of Vic Fontaine, wonderfully played by James Darren, added a truly unique twist to their cast of characters and a very positive one. And then there is that one line from Katheryn Janeway to the poisoned Borg Queen in "Endgame," their final episode: "Must be something you assimilated."
I have seen every episode of every Star Trek series. ST: DS9 and ST: Enterprise were my least favorite series, but I still enjoyed many of the episodes from both.
My favorite episode from Enterprise was "Unexpected." The shower scene at the beginning was hilarious. Overall, though, it was just a really entertaining episode. I also enjoyed "Hatchery", "Two Days and Two Nights", "A Night in Sickbay", "Precious Cargo", "Bounty", "Harbinger", "Observer Effect", "Affliction", "Divergence", and "Bound."
Of the orignial Star Trek series episodes, my favorite is probably "Assignment: Earth" (although it was really difficult to pick an absolute favorite). I greatly enjoyed "Shore Leave", "This Side of Paradise", "The Devil in the Dark", "Errand of Mercy", "Metamorphosis", "The Trouble with Tribbles", "By Any Other Name", "Spectre of the Gun", and "For the World is Hollow and I Have Touched the Sky" as well.
It is extremely difficult to pick a favorite for Next Generation. A favorite. I can't do it! How about favorites? My absolute favorite episodes are "Devil's Due", "True Q", "Ship in a Bottle", "Attached", "Parallels", and "Genesis". My other highly preferred episodes are "Time Squared", "Who Watches the Watchers", "Cause and Effect", "The Chase", "Phantasms", and "A Fistful of Datas".
I had a similar dilemma with Voyager, but I have vowed to be strong. Well...I meant to be strong. Oh dear. Bad me! My favorites are "Threshold", "Demon" (hated the follow-up to this one, though), "Someone to Watch Over Me", "Tinker, Tenor, Doctor, Spy", "Fair Haven", "Spirit Folk", and "Endgame (part I and II)". Can you tell that I adore the doctor? I also deeply enjoyed "Time and Again", "The 37's", "Displaced", "Scientific Method", "Human Error", and "The Renaissance Man."
Although I didn't enjoy Deep Space 9 as much as Next Generation or Voyager, I was absolutely CRAZY about Dr. Bashir. Naturally, many of my favorites (I know, I know) highlight his activities. They are "The Quickening", "Fascination", "Melora", "Our Man Bashir", "Family Business", "Little Green Men", "Bar Association", and "Profit and Lace." Other episodes that I enjoyed immensely were "Looking for par'Mach in All the Wrong Places", "Trials and Tribble-ations", "Meridian", "If Wishes Were Horses", "Ferengi Love Songs", "Statistical Probabilities", "The Magnificent Ferengi", "Inquisition", and "The Dogs of War".