The pilot of The Sopranos had me hooked from the beginning. So did the first episodes of Gotham and The Americans.
Other pilots include those of Boardwalk Empire and Boss, which I’m sorry was not picked up for a third season.
Going way back, the pilot of the original The Untouchables was outstanding.
With comedies, Cheers!, Frasier, Mary Tyler Moore, and Big Bang Theory come to mind (especially if you compare BBT’s first pilot to the one that actually made it on the air).
The unofficial pilot of McHale’s Navy, “Seven against the Sea,” was also a great show. I don’t think anyone at the time thought it would become a series.
At that, can we count “The Man Trap” for STAR TREK, as it was the first episode aired? Kirk is clever as the fearless leader, McCoy snarks and makes a medical discovery the ever-logical Spock finds fascinating, Uhura is an officer on the bridge – yeah, Uhura’s black and female and nobody makes a big deal about it, she’s just good at her job and fluent in multiple languages – and there’s a mysterious creature on the rampage with appearance-changing abilities, but, hey, that’s life aboard a starship in the future so whadayagonnado? Transporters! Redshirts! Phasers set to stun! Scotty has a crazy thick accent! Sulu makes deductions and has a sense of humor! We are up and running!
Raises a couple of interesting questions: Which of the two actual pilots is better, “The Cage” or “Where No Man Has Gone Before”? Of the other two episodes available in September 1966, would “Mudd’s Women” or “The Naked Time” have made a better debut episode than “Man Trap”?
Of all the supervillains in Batman, I always thought Gorshin’s Riddler was by far the most psychotic! 
I thought that Mockingbird Lane was fantastic. They aired the pilot as a special, but unfortunately the series wasn’t picked up.
Sherlock’s pilot was the best episode to date. Voyager’s, too.
But I admire the way the writers were willing to put what was the climactic scene of the entire series in the first episode. All the rest of the series was denouement.
I’d say QUANTUM LEAP got it right.
People keep saying SNL ain’t what it used to be, so recall that first broadcast: opening monologue from George Carlin, and Weekend Update with Chevy Chase – and Billy Preston is singing “Nothing From Nothing” – and Andy Kaufman is pretending to sing “Here I Come To Save The Day” – and Dan Aykroyd and Jane Curtin are playing it straight, so John Belushi and Gilda Radner can hit it out of the park without saying a word – and there’s even what looks like a real commercial, for the silly idea of a razor with a third blade. “Because you’ll believe anything.”
And for the cherry on top, Paul Simon stops by to make low-key mention of how, if you tune in next time, you’ll see him reuniting and performing with Art Garfunkel.
I think I remember it said in a Roddenbury doc that the network put Mantrap as the first episode, which garnered bad reviews.
I go with the Fringe pilot.
Justified had me hooked from the moment Raylan shot Tommy Bucks a couple of minutes into the pilot.
Spock lying on a bed in Sick Bay, bleeding green blood: “Captain, the monster attacked me” (or words to that effect). In the original edit, there were also a lot of weird sound effects every time someone pushed a button on the bridge: “Whoop! Phweee! Whoop!” Neither was Shatner’s portrayal of Kirk in that episode particularly likeable. And watch the dead guy flinch when Sulu (I think) touches his cheek.
Not surprising it got bad reviews. 
Also won three Emmys all by itself. Aaron Sorkin’s writing was nominated for another Emmy, but he won for another episode.
+1
Will also agree with “The Sopranos”. I used to be a huge fan of this series, but IMO, it has not aged well. The pilot is still a very good episode, though. (Second only to “Pine Barrens”).
I will throw in “The Simpsons”. I believe the first 30 minute Simpson episode was the Christmas special, where Homer loses his bonus, takes a job as a dept. store Santa and takes his $13 dollar check (and Bart) to the dog track, where they bring home their dog, Santa’s Little Helper. I never saw the Simpsons before this show, and I still consider it one of the best Christmas specials ever.
I know they were first on Tracy Ullman, as shorts, but nothing more.
If the Christmas special was NOT the pilot, ignore everything I wrote after “Pine Barrens”.
The (first) Christmas special was the first 30 minute episode to air, but it wasn’ t the pilot. The pilot was the Babysitter Bandit episode, which came back from Korea with such horrible animation that the producers decided to redo almost everything. The episode was delayed so much it ended up airing as the first season finale.
The X Files pilot did a great job of introducing the characters to us and each other, and establishing the intriguing underlying story mythos (sure, the mythos devolved into crap by the sixth season, causing me to start preferring monster-of-the-week episodes, but it started out great).
The X-Files pilot and first season really have such confidence that they don’t feel like first season episodes.
FWIW I also preferred the Monster of the Week episodes.
Aaron Sorkin always makes great pilot episodes, even for his crappy shows. In particular, Studio 60 on the Sunset Strip, may have the most lopsided ratio of quality-of-pilot to quality-of-show that I’ve ever seen, and The Newsroom has one fantastic scene in the pilot episode and never reaches those heights again.
(Here is the opening monologue from the pilot episode of Studio 60, and here’s The Newsroom.)
I love Breaking Bad to pieces, but actually felt like the flashbacky nature of the pilot episode was a bit gimmicky.
I enjoyed Battlestar Galactica, but I feel like “33” exhibited both the strengths and weaknesses of the show. It was gripping and atmospheric, and well acted and well written, but looking back on it now, do we really know what was going on? Did it make sense for the Cylons to be doing what they were doing given what we ended up learning? If the Galactica suspected their jumps could be tracked, why didn’t they jump and then jump again immediately rather than waiting for the Cylons to follow them again? Etc. (It’s been a long time since I saw it, some of those questions might have been answered in the episode.)
YES! This is what I was going to say. We watched it before the miniseries, knowing very little about the show. It was completely confusing to watch–there was no character introduction, no setting establishment, nothing to help you feel centered and stable. And that was awesome, because as a viewer you were scared and off-balance and confused and therefore completely able to empathize with the characters thrust suddenly into an apocalyptic war with no rhyme or reason. One of my favorite episodes of the show.
The other episode I was going to mention: House of Cards, which my wife and I watched last night. We’d avoided it for awhile thinking it might be too skeezy, but after making it through the first season of True Detective, we decided we could handle it. And oh, the joy: Spacey and his lines seem made for one another, and I was giggling gleefully through much of the episode as he nom nom nommed the scenery. My favorite line: “I love that woman, more than sharks loves blood.”