JD Robb's In Death series is one of my favourites.
I love how Eve has evolved and how the story of how her beginnings makes her the person she is in every book (although I was not the biggest fan of the ones where she went back to face off with her parents).
With over 40 books in the series, there is a lot of history in the newer book with the relationships that I almost feel I know them. You know she will worry about her friends being involved, something that would not have happened in the early books.
Yet each book is standalone and makes sense to the friends I have loaned them out to, even if they did not read previous books.
I also like that although set in the future, it has not been taken so far into fantasy that the world doesn't make sense and includes her ongoing issues with the technology that takes over their lives