The first question is actually hard for me to answer, because I like stories with a beginning, a middle, and an end, in all of their forms, and that includes book series. (And television, too; the series I have loved almost all have strong arc components, elements that seem to have been planned out and that carry across episodes and seasons.) For a story to have an end, it has to, well, end. Otherwise you end up with something like Sweet Valley High, where the Wakefield twins have relieved their junior year several dozen times by now -- the characters never grow, the world never expands, actions don't have consequences, and what's the point in that?
That said, there are certainly book series that I enjoyed so much that I was sorry to see them come to their conclusion, even if the ending was satisfying. The Otherland series by Tad Williams comes to mind, and the first Chronicles of Amber by Roger Zelazny. Although it's not a series, strictly speaking, I could probably go on reading about Charles de Lint's Newford almost forever. Harry Potter, to a certain extent. Sandman -- now that one, I could have happily seen go on much longer. I suspect I will feel similarly about Naomi Novik's Temeraire books.
There are also single books that, while good unto themselves, I would love to see expanded into a series. "Sunshine" by Robin McKinley tops this list for me; it was a wonderful standalone, but so much world building went into it that I want to see more, more!
As for series I would like to see end immediately, the one that comes to mind are the Southern Vampire Mysteries (aka the Sookie Stackhouse books, aka "True Blood"). They started out entertaining, then got darker and weirder, and now they seem to be losing focus. I wouldn't mind if I thought Charlaine Harris had a destination in mind, but I'm not getting that impression at all. Time to wrap things up, and send Sookie strolling off into the moonrise with Bill already.*
And, of course, A Song of Ice and Fire. But that's only if "the series ends immediately" is code for "all of the books have been written and I can read them now right now". A small wish, only; surely that can't be too much to ask?
*I am actually not rooting for Team Bill, particularly; I tend to be Team Sam, or maybe Team Alcide. But Bill seems the most logical, given the way the stories have been trending. As long as it's not Eric, I'll be content.
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