So, I've recently finished watching through Buffy the Vampire Slayer, and I've put together a short list of my five favourite episodes:
The Zeppo - S03E13
There's an apocalypse going on, and most of the Scoobys are fighting for their lives to prevent it, but that is relegated to the B-arc as Xander's attempts to figure out what he can bring to a group that includes witches and werewolves. He faces problems that no-one else can help him with, and acquits himself as well as anyone could, and gets one of my favourite moments in the whole series: "I like the quiet". I'd pair this up with a scene in Potential (S07E12) in which Xander talks to Dawn about coping with being the one who's not special.
Hush - S04E10
Demons come to town and steal everyone's voices. The entire episode is almost entirely dialogue-free, leading to a very creepy atmosphere which is complemented by The Gentlemen, the villains of the piece. There's quite a lot of plot development that happens while the characters are so constrained (for example, Buffy and Riley discover that they're both monster-hunters). And the final scene - where Buffy and Riley can talk again, and they really need to, but neither of them can think of what to say, so they sit in silence together - is perfect.
Restless - S04E22
Technically the season finale, this is really an interstitial piece in-between seasons 4 and 5. The episode takes place in the main characters' dreams, as they are being stalked by an unseen enemy. We basically get to explore their psyche, and see Xander's fear that he can no longer understand his friends, and Willow's concern that people think she's still who she was four years ago and merely pretending to be grown-up.
The Body - S05E16
Buffy discovers her mother's corpse (dead of a brain tumour) and has to deal with the aftermath in a very human way. This episode has no score, and very few cuts leading to a hyper-real environment in which its very hard to disengage from the characters' emotions. I initially thought the final scene where Buffy fights a vampire in the morgue was out of place, but having thought about it for a few moments I realised that it's the reminder that despite the fact that your world has ended, your life goes on, and you still have to keep on doing what you do; had Buffy had a less fantastical calling, this would have felt much less out of place.
Once More, With Feeling - S06E07
A musical demon comes to town and makes everyone sing. Very exposition-heavy and plot-light, this episode would fall flat if the songs and their performances were less than incredible. This is really a mood piece, explaining the characters' emotions and fears. The only downside is that it made other shows somehow think that they could also do musical episodes, even though they can never come up with a good reason to have everyone sing their feelings.
OK, so most of those are episodes where they step away from the plot and allow the characters to come to the fore. I guess that makes sense.