I love series.
This page is a testimony to that and that are only the series I'm currenly reading. There are many different things I like about series, too many really to discuss here. So I'll give you my top three.
I like that you can follow a character's growth.In the course of a book, a character often changes a bit. But in a series, you can show so much more than in a single book. A prime example is the China Bayles series by Susan Wittig Albert. The main character, China Bayles, goes through many changes during the course of the series and this is reflected in how she thinks and acts. None of these changes happened overnight, nor in a single book. But over all the books the series paints a great picture of China Bayles.
I like that you can take a theme and spin it many different ways.Often times, books have a central theme. It's nice, but there are so many viewpoints and different explanations to a theme, that you simply can't use them all in a single book. In that case, a series is a great way to deal with it, and if you use the same setting and/or some of the same characters, the series will form a cohesive unit without being 'to-be-continued' stories with a red thread through the books. The Elm Creek Quilts series by Jennifer Chiaverini is such a series.
I like that you can stay in a favorite setting for more than one book.Sometimes a setting just strikes a chord within you. It's wonderful, a world to loose yourself in and at the end of the book you're sad to leave it. How great is it that you can return there because the book is part of a series? A great example of this is the world Rick Riordan sketches in his Percy Jackson and the Olympian series. The way he weaves Greek mythology with the modern world is superb and since I read through his first book in one sitting, I'm very happy that the rest of the series is on my reading list this year. They'll let me return to the wonderful world Rick Riordan has created.