How important is it for a book in a series to stand alone? I think this question has different answers depending upon the context. For example, as a member of the YALSA's Amazing Audiobooks for Young Adults committee, we hotly debated this topic as a judging criteria. We determined that it is not our place to critique the story of a particular audiobook. We are merely concerned with the production value. Therefore, even if we are lost in terms of storyline, if the production is off the charts outstanding it could still make our list. Since our list is used widely by librarians as a collection development tool, we've decided to make notes in the annotations whenever a title is part of a series.
But this got me thinking about doing in-person reader's advisory. I like to recommend series because I feel like the tween/teen gets more bang for their buck assuming that if they like one book in a series they will have many more to keep them busy and hopefully encourage them to explore other books written by that author. I can't tell you, though, how frustrating it is when I'm recommending a series and the first copy is checked out! As you know, there are some series that you just have to read in order.
If all authors did as excellent a job at recaping previous books as Alexander Gordon Smith does with his Furnace series this wouldn't be an issue. The first chapter of each book is always a thorough, yet surprisingly non-redundant, recap of the previous books. I'm reading this series marathon style - one right after the other - so the previous events are fresh in my mind, but I still value that synopsis. Even though my preference is that teens read these books in order, I would (and do) tell them it's ok to start with book two since book one is always checked out. I know they will go back and read it later...they're that good!