I read something awhile ago that's been niggling at me ever since. It has to do with the last Harry Dresden book, "Ghost Story" by Jim Butcher. It was this guy's opinion that the series had jumped the shark with this book, basically because the book didn't push the overall story further, it was just about Harry dealing with being dead, and everyone else dealing with Harry being dead, too.
This is an opinion that I could not disagree more with. I thought "Ghost Story" was brilliant. Starting off reading it, I was a little wary of a book in which Harry could not do magic, but in fact I loved the book to death. I'm really looking forward to re-reading it prior to the release of "Cold Days" in a couple of months.
So why did I like it so much, and why do I feel it was the very opposite of jumping the shark? In a nutshell, because the characters all developed. Plus I thought the plot was as good as any in the previous books.
For me, a series jumps the shark when the characters stop progressing and each book is just more of them doing the same thing over again. There are a number of series I've stopped reading because of that, and a number of TV shows I've stopped watching for the same reason. On TV, I've noticed that the characters tend to become characatures of themselves, endlessly playing the same note.
In "Ghost Story" the characters progressed with a vengeance. It's true that the book was quite different from the others in the series since in this one, Harry himself didn't know where things were at, and we spent a lot of time learning alongside him what had happened to these people since last time. But different is not necessarily bad--in fact, I think it's essential to keeping a series alive.