The subject of how TV series stories used to be episodic, versus today's multi-story arcs, popped up in the discussion on "Where Star Trek started to go wrong", and I thought about addressing it there, but then I thought it deserved its own discussion.
In the old, origial Star Trek series, stories were told one at a time, in one episode. The adventure happened, and then they moved on to something new the next week, rarely--if ever--referencing what had come before. This was done, mainly, to make it easier to show the programs out of order when (and if) the series got picked up in syndication. You didn't have to rely on having seen the previous episodes to enjoy what was going on in the one you did catch. Everything was clear cut, up front, and easily digested.
In Babylon 5, stories are told in longer, multi episode arcs. Characters are developed and situations introduced slowly, over a number of episodes. Each style has its obvious advantages and disadvantages.
Single Episode: A Quick story explores an idea or adventure and moves on with little or no change.
Pro: Stories are disposable. You don't have to know what happened before. They're easy to get into. Someone new to it can come in in the middle and not be lost. Every week is a new story.
Con: There isn't much room for development. Character growth is restricted. An interesting idea or story gets dropped before it can fully take flight.
Multi-Episode: An elaborate plot takes the viewer on a journey over several weeks or seasons.
Pro: Stories can be much more developed. Characters can grow and change. Plots and ideas can be much more intricate.
Con: They're difficult to get into. If you missed an episode you're lost. If you didn't watch the show from the very beginning, you're unlikely to start watching in the middle. It's difficult to change direction if new ideas or material occur.
The first shows I became aware of in the new style were Star Blazers and then Babylon 5. Now, it is interesting that Star Trek once tried a multi-episode story arc, but I think it was one of the main reasons that Trek fans hated "Enterprise." The "Xindi" storyline was interesting to start with, but it went on too long, strayed from the topic too far and was not particularly well written. They did do the "Dominion War" arc in DS9, which seemed to have been pretty well liked, but then that was just a knockoff of B5's "Shadow War" series.
To be honest, I've seen this a lot happening in web comics. A lot of them are long storylines instead of Gag-A-Day format. And in surveying these, I can say that some writers are strong enough to be able to pull off a long storyline. Some are not. Someone who is incredibly good at doing Gag-A-Day may not be able to transition to long storylines and vice versa. In my opinion, long storylines can be overused. They stop feeling like they've got a direction and just wander hither and yon, without actually getting anywhere or resolving anything. The writers just seem to be vamping for time until the end of the story, or to keep it going for as long as possible, or until they come up with a new idea.
And, I can tell you from experience, when you're faced with a deadline and you're stuck, it's a LOT easier to advance an established storyline than come up with a new stand-alone gag. The storyline gives you a framework to use for reference material, while gag-a-day strips are self-contained and, hopefully, funny. Of course, gag-a-day can also become painfully repetative, like most of the syndicated comics that have been going for years on the same five jokes, endlessly retold.
Babylon 5 my favorite example of the Multi-Story arc. However, in Season 5, they just didn't know what to do. They'd concluded the story with Season 4, and couldn't really come back from that. When they got the fifth season, they had no idea what to do with it. Now, looking at Star Trek TNG, I can't think of any episode really that I would have wanted them to expand upon, and if they had, I don't think the writers would have had ability to handle a big storyline. Oh, there were a few episodes where I felt frustrated because they never ever mentioned something again, but I just don't think they could have pulled it off.
For example: "Relics" The Enterprise finds an abandoned Dyson Sphere built by some fantastically advanced civilization. Mr. Scott is there, but still, nobody bothers to examine the Sphere. There's a throwaway line about 2 science ships going to investigate it, but that's it. To my mind, they could have made an entirely new Trek Series exploring the Dyson Sphere. (Heck, Niven stopped writing just about anything in Known Space once he'd come up with the Ringworld idea, and all his books from that point on were only about Ringworld.) But, the problem is, I don't think that the Trek writing team was up to the task of taking on that story and keeping it interesting and compelling.
In the web comic world, I've seen a lot of long storylines that just got too long, and didn't have enough interesting subject matter to sustain them. In order to make a storyline hold the audience's interest, you really have to have a hard hitting appeal. You need to have a clear idea of where your story is eventually going to end up. And, if you want a large audience, you need to have a pretty low common denominator subject that will appeal to many tastes.
That means, basically, you've got to have something that's going to allow for occasional big explosions. That means you've gotta tell a war story or something similar. Something that can go back and forth for years, and it's okay. A sweeping romance never works, because once the star-crossed lovers get together, the writers run out of things for them to do. So they break them up. What's the point in that, then? The audience has invested all this time in following these people, and they don't get the "happily ever after" payoff.
Believe me, it's tough! You couldn't do a multi-episode story arc about Cyrano Jones and the Tribbles.
Some things are just better as stand-alone gags.