"Saw: The Series"
Imagine that, especially on a medium like Netflix, HBO or any other channel where the grisly content wouldn't be a problem. But before I get carried away, it should be emphasized that it's not for that reason alone that I think Saw would make sense in that format.
I remember being fifteen and being heavily into the Saw franchise, and of course when inevitably questioned about why I was so fascinated with such a gruesome series, my response (and the response of many other like me) would invariably be: "No, no, I dig it for the plot". And looking back on it? I wasn't lying, and neither, I assume, were others who cited the same defense. In those months while I and the people who I interacted with on IMDb waited for Saw VI, it really wasn't just the brutality of the new installment's Jigsaw traps that I was getting excited for, but the idea that we'd seen an epic conclusion to Hoffman's arc, or get some closure on Dr. Gordon's fate.
The thing is, now I'm a little bit older and, in hindsight, I suspect that I was actually a lot more invested in the story than the filmmakers of the latter day Saw films were. I think I was a lot more in love with the cool concepts than I was with the execution.
As a primary case study, look at a primary plot of Saw V: an officer of the law is broken down by the senseless killing of the person he cares for more than anyone in the world. He becomes despondent and in his desperation for justice, he murders a man and stages it to look like the work of a serial killer. Of course, the killer doesn't take kindly to this and blackmails the detective into an apprenticeship. Now that's a very interesting premise, and if all the fan theories we used to see overflow on these boards every year were proof of anything, they were proof that there's no shortage of directions you could take such a premise. A lot could be done with it.
Now, look at Saw V as a finished product. Does anybody really think that's a piece of cinema that does its concept justice? Did anybody honestly come out of that fifth installment thinking "Oh, yes, now there was a film that made the best of the premise it had to work with?"
Those interesting scenes with Hoffman and Jigsaw, the two learning to work together and the latter teaching the former his method; those scenes make up - what, twenty minutes of the fifth film? The best part is buried under the obligatory "fatal five" game A-story that doesn't actually culminate in anything besides a need to meet the annual gore quota.
Or, for another example, look how much plot that they tried to cram into Saw IV at the expense of a coherent film. Imagine what they could have done with that over the course of, say, an eight-episode season. For things like the flashback arc you could have a longer, steadier buildup to the clinic incident that would give the rest of the flashback arc more contrast (i.e, a stronger portrait of John before and after the loss of his unborn child, the true transformation into Jigsaw*).
Like most movies, these sequels were really only as good as the time and budget allowed, and when nearly half of each film's runtime is devoted to some game that showcases cool torture props but doesn't advance the story (although, let's face it, the sixth movie getting all political was kind of neat), then a good solid exploration of these potentially interesting characters or the story will almost always play second (third? fourth?) fiddle.
Now, having said that, imagine Saw as an episodic thing without the runtime constraints. In addition to all the cool traps and nastiness, you could have breathing room to more coherently explore this universe, or make more sense out of the motivation of characters like John, Hoffman or Amanda. As no shortage of writers from our current age of television have demonstrated, it's a great format to make the story more engaging. I think it would be an appropriate medium for the material, even if it means a clean slate reboot a la what Bryan Fuller and NBC did with Hannibal.
And let's be frank, can any continuation of the franchise - whether it's another cinematic venture or a TV series - be more embarrassing than Saw 3D? Really, at this point what's the worst that could happen (...I mean, I guess we already know the answer to that...)?
*Consider another cancer-stricken-family-man-gone-to-the-dark-side, Walter White, and how much more dramatically satisfying it was to see his character very carefully and patiently fleshed out over five seasons than it would have been if Breaking Bad had been a string of ninety-minute movies where, half the time, he only kinda sorta got to be the focus of the narrative.
That son of a bitch! Don't get me wrong, he's a fine writer.