There was a recent podcast of Nancy Pearl's Book Review with the theme, "What fictional character would you like to meet?" It was an interesting discussion, and the callers came up with quite a few interesting characters they'd like to meet in person, and maybe find out what happened after the book ended. Some suggested "bad" characters that they didn't exactly want over for dinner, but they still wanted to get to know them better.
One caller had a nice turn of phrase to describe characters you become invested in. She had just completed the seventh book in a series, and the last book in the series so far. In describing her attachment to the characters, and the disappointment in finishing the last book (so far), she said, "I feel like I have friends who aren't talking to me anymore."