I love Michael Connelly's books for this reason. Tess Gerritsen is another favorite. On TV--well, that's pretty easy. There's Bones, Leverage, and the new Perception (boy, did that series find its groove toward the end!).
From the writer's perspective, I love writing series characters. As I start thinking of the next book in Linc's adventure, I already look forward to hanging out with Henry and Ben, and Linc's family. It's like meeting old friends, and finding out what's new.
What's your favorite series? Why do you love those characters so much?