…name your SINGLE favorite episode. No hemming and hawing; no lists. Just one.
Mine’s Lisa’s Wedding. Perfect balance of sweet and funny with a huge dose of imagination. Plus I love the end where Lisa walks away with a new appreciation for her Dad.
Shari Bobbins. Never fails to crack me up.
“Baby on Board” Barbershop Quartet - official name ***Homer’s Barbershop Quarte***t.
Mine was the X-Files episode. Although most of my other favorites were WAY before that season. I just liked it for some reason. “Homer’s a Dope”.
Oh, great one!
I do not know the name of the episode, something like 25 Scenes in Sprinfield, but it was a bunch of vignettes, one which culminated with Nelson parading through Springfield in his underwear waving to the crowd.
There are a bunch i could name, but the OP just wants one, so i think i’ll go with Homer’s Phobia. Can’t go wrong with John Waters.
“22 Short Films about Springfield,” which was parodying the movie 32 Short Films about Glenn Gould.
that’s impossible to answer.
“22 Short Films About Springfield” - of which there were only 21, and that’s if you include Professor Frink’s appearance at the end. (There was a 22nd one cut from the show, with Ralph and Krusty on a plane; part of it aired in a commercial for the episode.)
My choice: “Radio Bart” (the Timmy O’Toole / Bart falls down a well episode) from Season 3.
Mulder: What’s the purpose of this test, Scully?
Scully: Nothing. I just thought he could stand to lose a little weight.
I have that episode on VHS, believe it or not, and the kids and I watched it a couple of months ago when I got my old VCR out.
My favourite is 8F13, “Homer at the Bat”. That’s the episode where Mr. Burns hires a bunch of MLB ringers to come in and play on the company softball team so they can beat Shelbyville’s team.
Dr. Hibbert: Good Lord! Gigantism! 
King Size Homer, the one where Homer gains 61 pounds to get on disability and work from home. That episode is packed with great quotes:
“Bad news, Dad. We’re out of food. We’re even out of the basic elements of food. You ate all the tarragon and you drank all the soy sauce!”
“I don’t want to look like a weirdo. I’ll just go with the muumuu.”
“I wash myself with a rag on a stick!”
“Hey, fatty! I’ve got a movie for you! ‘A Fridge Too Far’!”
“Homer, your bravery and quick thinking have turned a potential ‘Chernobyl’ into a mere ‘Three-Mile Island.’”
“Hey, Miss Doesn’t-find-me-attractive-sexually-anymore, I just tripled my productivity!”
…and of course, “The fingers you have used to dial are too fat. To obtain a special dialing wand, please mash the keypad with your palm … now.”
Bart the Daredevil. From the Truckasaurus commercial, to Captain Lance Murdock, to Homer falling into Springfield gorge not once but twice, there are more laughs packed into these 22 minutes than I’ve seen on any show, ever. (Well, until Archer came along, maybe…)
My pick is Cape Feare, which doesn’t have any emotional content to speak of but just cracks me up harder than any other episode in the whole canon. It was written at the end of the fourth season (it aired early in season five) when the writing staff was exhausted and most of the original writers were getting ready to leave the show. So they went nuts and packed the episode with stuff like Homer’s Witness Protection blunders, Sideshow Bob’s German tattoo, his performance of the HMS Pinafore complete with costumes and a Playbill, Homer accidentally scaring the crap out of Bart by bursting into his bedroom with a knife (and then doing it again with a chainsaw and hockey mask), and the scene where Bob is run over by an agonizingly long parade. The parade is my favorite, particularly the very inefficient writing on the elephants who trample Bob. And, of course, this is the episode with the rake gag.
I don’t remember the name of the episode but it’s the one where Gabbo the dummy and the ventriliquist come to town.
I’ll go with “Marge vs. the Monorail”. Because Batman’s a scientist.
(I tried to add this to my earlier post, but by the time I looked everything up, the 5-minute limit on editing posts had expired.)
Oh, and kudos to Fox for actually making the “500th episode” the 500th episode aired. With Fox’s “creative accounting,” you can never be sure.
(Cases in point: the “300th episode” was the 302nd to air (and they even joke about it during the episode), because (IIRC) they wanted it to air on the same day as Fox’s Daytona 500 coverage (only the second time Fox had aired the race), so they explained it away as, “Well, it’s the 300th episode produced since the show became a series (so the Christmas Special doesn’t count)”; the “350th episode” was the 351st to air, but they wanted it to air the day that Family Guy returned from its (second) cancellation. Also, the 400th episode to air was not the 24 episode but the one that followed it that night, but, to be fair, Fox never actually said that the 24 episode was #400 (at one point, it was scheduled to air as #400, but that would have meant airing it 30 minutes after the show’s regular time slot).)
“You Only Move Twice” - Hank Scorpio, hammocks, flamethrowers…what’s not to like?
Krusty Gets Kancelled (the Season 4 finale)
That’s one of my favorites.
But my pick would be the one where Homer gets bypass surgery.
So many memorable lines in that episode!
Homer and Apu.
Who needs the Kwik-E-mart