I think that every good tv show has the character episode some time in the first season. I think it is the single most important episode for every tv show. The character episode is the episode that opens up and truly begins the development of a special character on the show. Usually this is done through a previously undisclosed history. This is the episode where they sell the character of interest to the audience. This is what develops into a true following and separates the show from others out there. Even if the show is episodic in nature, like a sitcom or a monster/case of the week type of show, there needs to be an overall arc in the development of the character and this, in my opinion, is what makes or breaks a show.
Some recent episodes of this nature that I remember from my favorite shows include:
Three Stories (House Season 1 Ep 21)
As much as people like the medical mysteries, I think the majority of people tune in for the character interaction and most of all for Hugh Laurie's portrayal of Greg House. Not only was the story-telling great in this episode, but this is when you found out how House came to be. This episode actually won a writing Emmy, and is one of the episodes of House that I never tire of rewatching. Then again, if you didn't like this episode, I doubt you would have continued on with the series.
Game Night (How I Met Your Mother Season 1 Ep 15)
Another example of great story-telling, this time the viewer was given the backstory of how Barney Stinson came to be. Even with a talented ensemble cast, the character that always stood out was Barney and this episode allowed the viewer to connect with him and his story, and not just treat him as the wacky comic relief that spat out crazy theories. While NPH was fun in Harold and Kumar, this was the show that really brought him into the national spotlight (would you say again? I mean, we all remember Doogie Howser, right?) and led to him hosting the Tonys and the Emmys.
College (The Sopranos Season 1 Ep 5)
The Sopranos was a revolutionary show, and this was probably the most memorable episode from that spectacular first season (it was for me). This episode did not look to the past like the ones listed above, but rather looked to the future as Tony drove Meadow to college interviews. The episode was the one that really opened up Tony as both the loving father and the future mob boss and set the tone for what the show was really about: Tony being at the center of both those families and how he deals with it.
I'm sure there are many more and would welcome any additions in the comments. Also, my favorite show in the fall season so far has been Castle. The actors have good chemistry, the case of the week usually has enough twists and turns to keep you guessing for a while, and it's very light and the perfect dramedy, a name that I haven't really used to classify a show since Boston Legal.