Thoughts on Writing a Series

I'm always up for a good series. I like them, because if I really am fond of a book, I don't want it to end! Since I wrote Book II of the Nightshade Chronicles (which comes out any day now), I've been thinking a lot about series, and what makes one successful against another.
Recently, I read a middle-grade series that started off great. The first and second books were really entertaining, and the third book was good, though I did skim a little with that one. By the fourth book, the writing felt completely different--and not in a good way. The author seemed genuinely bored with the plot, and the writing was rambling and clunky, not to mention the book was 500 pages. The story seemed to be copied from the first two books, just with different characters and settings, even the action sequences reeked of past scenes from earlier books. It was a real disappointment, at least to me, though I'm sure others loved it.
When I had a talk with my editor about Book II, she told me flat out the book has to be super special, perhaps even more so than the first. That was kind of a light bulb moment for me. Readers want what they read in the first book, but they don't just want a continuation; the book needs to be extraordinary on its own. I think if you're going to write a series, each book needs to be standalone great! Characters need to evolve, as does the story...not just continue.
What is your take on writing an amazing sequel or series? What are some series you've read that were in your opinion successful?
Oh, and I really just liked the cat in the above picture. Don't think I'm hinting that I didn't like the Harry Potter series! A. I've never read it. B. I don't want hate mail!!  ;)