Firefly: “Out Of Gas”. That was the first Firefly I ever watched, and it was a perfect introduction. Complex structure - flashbacks within flashbacks, and it essentially told the story backwards - but all in the service of good storytelling, and never too clever for its own good: by the end I just wanted to know more about all these people, where they were and what their relationship to each other was.
Seinfeld The Contest (if I recall the name correctly).
“Are you king of the castle?”
Dr Who: Blink
Clever plot; the Doctor not the centre of the story; whimsical and exciting. 
Sliders: The name of the particular episode escapes me, but it’s the one with the ATM’s that automatically enter you into the “Death Lottery.”
I think that’s their best ep to date.
Arrested Development: The One Where They Build a House
Why they were using Friends-style titles I don’t know, but this is where the show started to peak. It’s got wild gags that work even if you haven’t watched older episodes, Iraq war satire, the Blue Man Group storyline, “Her?” and some funny stuff from everyone.
Possibly. The one where Bobby moves into the dog house would be my vote. Or the one where Luann becomes a born-again virgin.
Seinfeld is a tough one. There are so many excellent episodes. I’d nominate the one where Elaine dates the mimbo and Kramer has phone sex with Jerry’s girlfriend. “I can’t spare a square.”
Futurama - Amazon Women in the Mood
“No can dunk, but good fundamentals, make it more fun to watch.” I was already a fan, but if I had never seen this show before and I saw only this episode I would have been hooked. I think the OP is looking for an all encompassing episode…this isn’t it, still, thats my pick.
Heroes: Company Man
Absolutely.
Scrubs: My Screw-Up. Brendan Fraser returns from a world tour, and they check on his leukemia. It’s also Jack’s first birthday party. If you’ve seen the episode, you know what I’m talking about.
DS9: In the Pale Moonlight. Sisko is recording a log entry on how the Romulans entered the war against the Dominion. It’s the first Trek episode where the captain got his hands dirty, and doesn’t apologize for it, and would do it again.
Both of these will kick you in the gut.
West Wing: I will nominate Two Cathedrals. (I think that’s the name of the episode.) At TWoP says, “It’s not King Lear or The Book of Job, but it’s as close as you’re going to get on primetime television.”
For B5 I’d nominate A Late Delivery From Avalon. A good character study of most of the leads, with a really nice A plot
Any episode of Six Feet Under, I was hooked from the beginning! The one where Nate finds out that Lisa’s BIL was involved in her murder was especially good, and the episode when Gabriel flips out and disappears was great.
It’s my favorite episode too, but it’s so disjointed though I think it would be too confusing for someone who hadn’t seen it before.
I’d start out with Ghosts of the Sargasso from Season One. It opens like a typical Jonny Quest/Scooby Doo adventure, then falls hilariously apart as everyone involved (except for Brock of course) is revealed utterly pathetic. It’s got Dr. Venture pere, David Bowie references, and a Dr. Orpheus cameo.
“Tom? It’s your wife, sweetie. You’re dead now.”
Then, when they’re hungry for more, **Mummies ** … .
Newsradio: a couple of choices.
–Smoking: Battle of wills between Dave and Bill over the new no-smoking rules in the office.
–Super Karate Monkey Death Car: The title alone is a winner, plus Ron Jeremy in a cameo.
–Complaint Box:
I know it’s a stretch of the premise, but…
If you want to watch just one WWII movie, watch Band of Brothers.
Oh wow, when I saw the thread title I thought of this very episode. It’s actually my favorite single episode of any series I’ve ever watched.
agreed
I cry laughing at “I lost my shoe!”
That;s the one I hooked my wife with. She was leery of watching a show I was so geeky about, but that episode sold her.
Farscape: Either “Crackers Don’t Matter” (funny as hell) or Family Ties (Season one ender - it’s an amazing episode).
Based on the OP (the hypothetical viewer only gets to see one episode), I think glee got this one right. Two Cathedrals is a better episode of the series, but it requires a pretty decent knowledge of the characters & background for the punch to really hit home. The episode just before it (18th & Potomac) has the most amazing wordless 15 seconds of tv ever (Leo’s face when he gets the news of Mrs. L’s death).
In Excelsis Deo is much more self-contained. All you really need to know is that Toby and Mrs. Landingham are the resident curmudgeons and that comes across just fine in the episoide itself.
I also have a soft spot for IED since I have a cast/director/producer signed shooting script of it.