I'm ambivalent about series--whether they be books, movies, or TV. I want series characters to grow and change organically, not repeat themselves too often. If they change too fast, though, the series is bound to be shorter.
What's your preference as a reader/viewer? If you're a series writer, what's your approach? I've written five stories in a series about a 1930s pilot-for-hire. I've tried planning them in advance, but have had the most success listening for my protag's voice and writing the story he's prepared to tell. So far the stories have jumped around in time ala Mosley's Easy Rawlins. This strikes me as one way to keep things fresh.