I don’t know, I introduced all my university friends to MSTSK with Cave Dwellers which is still our favorite episode and we still borrow riffs from it to this day. 
I still have this episode on my PVR, it’s freakin hilarious. I loved the marionette scene where they recreate the move and Daniel Jackson draws all over the screen with a marker. Classic!
For Firefly, the actual pilot. Except it’s a two-parter. But I bet the first part would hook you enough.
Kyla said:
Oddly enough, the one I wouldn’t show is The Train Job, you know, the one Fox ran as the pilot. About the only thing that worked on that one was the ending, where Mal
kicks the henchman through the engine
Even though that is dumb for a lot of reasons, it really cements who Mal is, that he doesn’t put up with stuff. But other than that, that episode was weak.
Yes, it’s a series that you need to watch several times, because there’s no way that you could understand much on first viewing. So I’d agree that it has to be episode 1 of FLCL, because the later episodes just get weirder.
DS 9 “In the Pale Moonlight”
this was a wonderful dark episode where the hero is non heroic and presents wonderful moral dilemas that the previous incarnation (Next Gen) avoided having its protagonists deal with. Even Avery Brooks isn’t as hammy as usual and puts out a great performance
That’s not fair. The person you showed it to would end up looking high and low for another ep that even came close and would never find it in a million years 
My vote is the same as from that thread last week where we listed the best-written episodes from the best-written shows or something. It’s Peep Show’s series 1 episode 3, where Mark and Jez go bowling with neighbor Toni and a teenage girl that Mark met at a party. Sophie and Jeff show up. Hilarity (and penis) ensue.
Absolutely agree with the previous poster re: “In the Pale Moonlight.”
Firefly: Either the real pilot or “Jaynestown.” Or “Out of Gas.” Or “Our Mrs. Reynolds.” Aw hell, it doesn’t really matter - they’re all great, and the series is only 14 episodes long.
Scrubs: Any of the episodes guest-starring Brendan Fraser, but especially “My Screw Up.” These episodes are probably the purest distillation of all the factors that made early-seasons Scrubs so great.
The Office (US): “The Injury” or “The Client.” Season 2 was easily the best season of the show, and just about any episode would probably work, but these two episodes best show off the ability of the show to derive unexpected humor from the characters’ interactions.
Buffy: “Hush,” no question. It’s more of a stand-alone than the other truly great episodes, and really gets the point across to a new viewer that this is a show with ambition.
Veronica Mars: The pilot. The show is generally too serialized for a new viewer to “get” starting halfway through. But it helps that the pilot is, on its own, one of the best episodes of the show’s stellar first season.
Battlestar Galactica: “33” (assuming you can’t get them to sit through all four hours of the miniseries). Simply put, one of the best hours of television ever created.
Futurama: “The Luck of the Fryrish”
How I Met Your Mother: “Slap Bet” (or the aforementioned “Pineapple Incident”). But I’d give the edge to “Slap Bet” for the hysterical faux-80s music video.
Was one of the best episodes of DS9, but wouldn’t be a very good way to introduce the show IMHO, as it depends on the watcher knowing a fair amount of background about both the show and the characters.
The Simpsons - definitely Homer Badman for me. Straight through hilarious.
Flight of the Conchords - Mugged. Two of their best songs and a great plot.
Frasier - The Matchmaker
Confusion ensues at the Crane household after a gay station manger, Tom, is hired at KACL. Frasier plays matchmaker for Daphne, unaware the he is in fact the one Tom is interested in.
The X-Files: “The Last Repose of Clyde Bruckman.” Everything The X-Files was capable of doing, all done excellently. IMHO, one of the best hours of television ever broadcast.
Remington Steele: “Steele Crazy after All these Years.” Creepy and spooky, and with some of the best Steele/Murphy dialogue.
Quantum Leap: “The Leap Home, Part II.” Completely, utterly, heart-breakingly beautiful.
Lost - the pilot episode, of course, should be seen first and it is damn good. And while I would say that it is pretty vital to watch the entire series in order, if I had to pick one episode other than the pilot to hook someone, it would have to be “The Constant.” When Desmond finally reaches Penny on the phone at the end… well, rarely does a television show move me emotionally as much as that.
I’m gonna have to agree with whoever said Walkabout for Lost. It’s a great episode early enough on in the season so you don’t need to know anything other than "a plane crashed on the island and there’s some sort of monster in the jungle. The final scene really shows that this is not a normal show.
X Files - Bad Blood! Love this episode and think others would too.
Six Feet Under - Pilot.
The L Word - Pilot.
Malcolm in the Middle - Rollerskates. Nuff said!
Buffy - Hush is the obvious choice; coincidentally just re-watched it with my kids
Star Trek TNG - Yesterday’s Enterprise: in a single ep (unlike the season-spanning cliffhanger with the Borg) you get all the TNG goodness you can handle, including Worf loving prune juice as “a warrior’s drink.” My favorite ep, but a perfect distillation of TNG-ness…
Lost - Further Instructions/Walkabout (Really any Locke-centric episode.)
Agreed. A better candidate would be the first season episode Duet. The episode gets to the heart of one of the central conflicts of DS9. All the backstory you need for the protagonist (Kira Nerys) becomes apparent in the episode. Duet is a well written self-contained episode that avoids the wishy-washy feel-good ending that plagued TNG.
You can view the episode on youtube here.
No, not fair would be telling someone to watch the “chicken pot, chicken pot, chicken pot ppppppppiiiiiiiiieeeeeee” episode of “Just Shoot Me,” and have then looking high and low for another ep that even came close and would never find it in a million years
For which we can all be eternally grateful. David Cross has to be one of the most annoying people on the planet.
Seinfeld - “The Contest” of course.
**Friends **- Probably the one where Ross is trying to get everybody ready to go to his awards ceremony. Joey and Chandler get into a clothing war, and Rachel goes commando.
I was never really a fan of the X-Files, but in a similar spirit to the OP, a friend insisted I watch the episode “Home”. I did, and LOVED it so gave the show a try, but I never found any other episodes lived up to that so I eventually gave up disappointed.
For LOST, I would say whichever episode the polar bear first showed up in (was it the pilot?)