My answer is not much, and that's not a criticism, because I don't like what gets called "serialization" these days. I always heard that DS9 was the serialized show, Star Trek's soap opera, so I didn't make an effort to see it, and when I finally got the chance, I was pleasantly surprised by how episodic it is.
The obvious exceptions to my observation were the last nine episodes of the series, the first six episodes of Season 6, and arguably the three "Circle" episodes of Season 2. Apart from those, the episodes typically told stories that resolved themselves in one or two parts, and from episode to episode, the focus shifted to different characters, giving the series variety. And one of my complaints about so much serialized TV on today, by contrast, is the lack of variety in the episodes, the way they all blur together in theme and focus, a problem compounded by the fact that individual episodes never structurally end. They just stop playing when the 42 odd minutes or so of show time are up. Deep Space Nine episodes were more structured, even when they were a part of something larger.
Yes, there were consequences for the characters from episode to episode and season to season. Sisko got a promotion (though this wasn't the only Trek series with a rank change). Odo courted Kira and Dax courted Worf (plenty of that kind of thing in other Trek shows). The major antagonist groups and characters were handled with an artful consistency, as was the period of time during which Odo lost his shape shifting abilities. But if this is "serialization," it's serialization of a different (in my opinion preferable) kind to diffuse plots that stop midstream and get picked right up when episodes begin and end, sometimes punctuated with the most manipulative of soap operatic devices, the cliffhanger.
The obvious exceptions to my observation were the last nine episodes of the series, the first six episodes of Season 6, and arguably the three "Circle" episodes of Season 2. Apart from those, the episodes typically told stories that resolved themselves in one or two parts, and from episode to episode, the focus shifted to different characters, giving the series variety. And one of my complaints about so much serialized TV on today, by contrast, is the lack of variety in the episodes, the way they all blur together in theme and focus, a problem compounded by the fact that individual episodes never structurally end. They just stop playing when the 42 odd minutes or so of show time are up. Deep Space Nine episodes were more structured, even when they were a part of something larger.
Yes, there were consequences for the characters from episode to episode and season to season. Sisko got a promotion (though this wasn't the only Trek series with a rank change). Odo courted Kira and Dax courted Worf (plenty of that kind of thing in other Trek shows). The major antagonist groups and characters were handled with an artful consistency, as was the period of time during which Odo lost his shape shifting abilities. But if this is "serialization," it's serialization of a different (in my opinion preferable) kind to diffuse plots that stop midstream and get picked right up when episodes begin and end, sometimes punctuated with the most manipulative of soap operatic devices, the cliffhanger.