My Top 10, with just 4 shows, and counting 2-parters as one long episode...
10. "The Red Circle" from: Granada's Sherlock Holmes TV Series with Jeremy Brett
A number of Holmes' mysteries could count as my favorite, so this might be more of a "mood pick," but of the cases Brett had the opportunity to do, this is one of my favorites, and it has everything a great Holmes mystery has--an energetic, logical, sometimes snappish and often-sarcastic Holmes, an ever-steadfast Watson, some nice innocents in distress, a deadly villain, and a tough mystery to solve, with action and the powers of deduction leading the way!
9. "The Apple" from: Star Trek (Season 2):
I just love this episode...and it's not one that gets too mcuh attention from Trekkers, but I love it--my favorite characters, Chekov asn Spock, play big parts, almost everyone's there, and the dilemma's so intriguing...Garden of Eden vs. Progress...
8. "The Final Problem/The Empty House" from: the aforementioned Holmes series
It's Sherlock Holmes vs. Professor Moriarty in the epic battle, and then Holmes' return in Part 2--enough said.
7. "Three Stories" from: "House" (Season 1):
If you've never seen "House"...WHAT'S WRONG WITH YOU?! ;) Easily the character today I identify with most, far and away, good traits and bad, and the only show I watch today, House, the show and the man, are incredible--and this is the story of how he came to be that way, how House became House, in part, by requiring his famous cane. Throw in the fact you get all this wrapped in a package of humor, great pacing, and not one but THREE medical mysteries for the price of one, as well as Holmes, er, House's answer to Sherlock Holmes' Irene Adler, Stacy, and this easily fits the #7 spot.
6. "Darmok from: "Star Trek: The Next Generation" (Season 5):
Captain Picard meets an alien race that FINALLY can't communicate with humantiy via that plot convenience Trek--and really most of sci-fi--uses to explain why creatures spawned light years away converse easily, the universal translator (or, I suppose if you wanted to take a comedic turn here, the Babel Fish works here as well.) And just HOW does this alien race communicate? Via metaphor...referencing their old literary and mythological works. That's right, Picard meets a race of English majors! ;) But it's a great show about communication, the value of such stories, how different and yet how similar we are, and so much more...I've even seen some doctors write up thesis reports on the show pertaining to the mythological element, particularly as the always-awesome Patrick Stewart, as Picard, tells the Epic of Gilgamesh--for those curious which part, Gilgamesh meeting Enkidu and then their quest together--to his dying alien friend. POWERFUL stuff.
5. "Son of Coma Guy" from: "House" (Season 3):
I'm actually watching this right now, and it's jsut as good as ever--House needs to solve a case, but to do it he must first wake up a man in a vegetative state, which he does, but the man will only stay awake for 24 hours before essentially going back into a vegetative state of no return again, and he wants to go on a road trip and eat and be merry for his last day. House is ALSO in the middle of a criminal investiagation, as a detective made sour by House--long story short, the detective told House where he could stick his rude behavior and House stuck a thermometer there...and left it there two hours--is trying to nail him for his Vicodin possession, and Wilson just lied to the cops for House and is nervous about that. Coma Guy, House, and Wilson's road trip serves as a character exploration of all three--why Coma Guy feels so sour about his son dying (he was a businessman and so used to controlling everything and feels miserable that he couldn't protect his family from a fire and now can't save his son AND now can't even control his fate), why Wilson is truly angered by House at the moment (House treating their freindship trivially and pushing it until it breaks, which is confronted perfectly in the climax) amd why House, man who is so bitter towards people, chose a career that has him constantly dealing with them (and THAT story is so good and such a perfect backstory I'll leave it for you to find out.) It's finny, it's heartfelt, it's sarcastic, it's thoughtful...and when the cimax finally comes, it does NOT disappoint, as all three play pivotal roles, and it's neither a happy nor sad ending, but rather one that leaves you talking...the BEST kind of ending.
4. "All Good Things..." from: "Star Trek: TNG" (Season 7, series finale):
Simply beyond words...but all good things MUST come to an end--and Star trek: TNG did with a finale that ranks as one of the best TV finales in the last 30 years or so...and if you've ever had friends drift away, or worried about what might happen over time...this is all the more the episode for you.
3. "The Best of Both Worlds" from: "Star Trek: TNG" (Seasons3-4, season finale-premiere)
The infamous cliffhanger and resolution...watch the episode...resistance is futile! ;)
2. "House's Head/Wilson's Heart" from "House" (Season 4, season finale):
It's a mystery worthy of Holmes and House. It's a heart-wrenching situation worthy of Watson or Wilson. The titles are the BEST on this list--House's head, Wilson's heart, it mirrors the individuals so perfectly, and with the patient being not just some one-shot patient-of-the-week, but an established character, and one with an established relationship with Wilson and a rivalry with House, how and why House is involved, how we LEARN about all of this, the bus crash scene (watch it, AMAZING effects, that ALONE, I hope, got this episode an Emmy nod for something) and the final, shocking resolution, with House and Amber having that last conversation in what an atheist like House would call "a chemically-induced state of hallucination" and what a theist would call "nothing short of Limbo itself," this is simply INCREDIBLE, and after the mediocre season #4 had been--especially when compared to #1-#3--this gave "House" a fresh shot in the arm, and well into Season 7, it's still going strong--just like this two-parter for the ages.
1. "The City on the Edge of Forever" from "Star Trek" (Season 1):
This is THE episode of Star Trek. If you've never seen Trek and wonder why millions love it...THIS is the episode to wathc. I always tell folks, who've never seen Trek adn want to give it a shot, to watch this one, not just because it's widely held as the best--though "The Best of Both Worlds" and, if you're a DS9 fan, "In the Pale Moonlight" both ahve arguments, the latter jsut missing this list, consider it the Honorable Mention of this list--but because it's the CORE of Trek without all the potentially-off-puting gadgets and spaceships and jargon and aliens. Plain and simple: this is Kirk, Spock, and McCoy, along with Edith Keeler--done by the always-elegant Joan Collins--in a story that's a mystery, a lvoe story, and one of the most gut-wrenching moments in all of Trek, and one ANYONE can identify with, coming down to Kirk keeping the love of his life or preventing Hitler from taking over the world. Love vs. Logic, Edith vs. Spock...and all on the great captain's shoulders in 50 minutes that end leaving Kirk, and the audience, both feeling as if they've been punched in the gut...and yet so very much in awe.