I've come to a funk at least a couple times with a story's end. Can't clearly remember the first one (maybe Welcome to the N.H.K., but I doubt it, retrospectively), but I got this way when I caught up on the then 70 chapters of Kodomo no Jikan (side note: much as a "lol perv" I can be thanks to the Internets, this series, despite its, er, fanservice, actuals makes me turn away from entertaining such thoughts; the characters just grew on me that hard). Dunno how I'll feel once I finish A Series of Unfortunate Events, though I'd still have the Beatrice Letters (and, if it ties in, the autobiography) to go through.
Lessee... The thing with some of my most liked game worlds, FFX/-2 and Chrono Trigger, is that they feel pretty well-worn and complete. Maybe the Dissidia 'verse, which especially hit me considering what I've seen and heard of Gilgamesh and Prishe so far (I have some GG scenes to still see); between Gilgamesh's direct tie to Bartz and his semi-ties with the other worlds he has or will show up in and Prishe's upbeat personality and history with the Warrior of Light, I wanna see more of the day-to-day of those guys, and see them reach a more fulfilling end.
That's probably what decides if I wanna see a story end: Have I spent enough time with the characters? The world itself might do this to me, too, but if a character endears to me enough that I just wanna witness their mundane lives and interactions, it hurts to see the (proverbial?) back cover close.
...maybe Hitchhiker's Guide and Dirk Gently, since we lost that great author mid*-production. Might hafta grab that sixth H2G2 book, see what was done with it.
*pfft, "mid".