I got in a discussion on Twitter about what the best "number" for an episode of a TV series to have might be. My initial feeling was that the middle of the third season was probably best: shows have settled into a pretty good groove, they know what they're good at, by sticking with the middle, that allows 13-episode seasons to work with 22-episode seasons.
So, using that logic, I poked at Wikipedia, and found several classics huddled around the 9th-12th episodes of the 3rd season of some of my favorite shows:
The X-Files might be at its best at this point. Its 3x09 and 3x10 are my two favorite mythology episodes, "Nisei" and "731." 3x12 is the excellent "War of the Corprophages," which might be my favorite overall.
Star Trek: The Next Generation has a pretty good set of episodes here, highlighted by 3x10 "The Defector," one of my favorites so far. On the other hand, 3x12, "The High Ground" is a completely ridiculous terrorist episode.
Buffy's season 3 is rightfully heralded as its best, and this is around when it started moving from good to great. 3x09 "The Wish" is a great episode, as is 3x12's "Helpless." 3x11 "Gingerbread" is very good, and 3x10 "Amends" is 2/3s of a classic, 1/3 horrible deus ex machina.
Angel's ninth episode of its third season is my favorite of the whole run, "Lullaby." Its next three episodes are good but not quite classic.
Babylon 5 has one of its strongest runs ending here, with the strong "Point of No Return" and the all-time classic "Severed Dreams" at 3x09 and 3x10. Its next two episodes are weaker, though.
I haven't gotten to this point in The Sopranos, but 3x11 "Pine Barrens" is usually considered among its best.
The Wire is finishing up one of its strongest seasons at this point. 3x09 and 3x10 build the tension to a breaking point, and 3x11 features the shocking death of one of its most important characters. All are great choices.
The Simpsons is also coming into its own, with two classics: 3x10 "Flaming Moe's" and 3x12 "I married Marge."
Arrested Development was, sadly, winding down, but included some great episodes. I really dislike the potential finale "S.O.Bs" at 3x09, but each of the next three are fantastic, especially 3x12 "Exit Strategy."
The Boondocks was very good throughout most of its third season, but has two transcendent episodes, 3x09 "A Date With The Booty Warrior" and 3x12 "Mr. Medicinal" which probably made me laugh harder than anything else that aired this year.
Finally, Battlestar Galactica may have been at its weakest here, oddly. 3x09 ("Unfinished Business") is excellent, but 3x10 "The Passage" could be my least favorite Jane Espenson script ever, and yes that includes "Doublemeat Palace." 3x11 and 3x12 have the confrontation on the algae planet, which wasn't bad, but turned the Final Five into a big thing. I didn't like that thing.
Based on all that, I lean towards 3x10 as my favorite, but I could easily be swayed to 3x09 and 3x12. Other people have suggested that 3x10 is good for Breaking Bad, Dr. Who, Lost, Futurama, and more, but I'm not expert on those, so cannot judge.
As a wildcard, I checked out 4x10, which could also contend: Buffy's "Hush," Angel's "Awakening," Battlestar Galactica's "Revelations," The X-Files' "Paper Hearts," and The Wire with a very good episode towards the end of its fourth season.
Only one other person suggested another collection of episodes, S2 E05. I don't watch most of the shows mentioned, so I can't really judge, but hey! I didn't do this alone!