Reading Series Out of Order

One of the gifts to librarians that designers/publishers can give is to put the number of the series book on the spine of the book, so that we can tell what order the series should be read. How annoying it is to have to look at front or back matter to find a list, or--even more time consuming--to have to research where a single book fits in a series.  If I can't determine where it fits by examining the book, I turn to the incredible Juvenile Series and Sequels database from Mid-Continent Public Library, where I can search by series title, book title, series subject, or book author.

How can one know if a book in a series can be read as a standalone book, without having read the titles that come before?  My general policy is to read at least the first book in a popular series--but I don't feel compelled to read every single Magic Treehouse book (I get the idea...).  I certainly don't want to give a kid Harry Potter and the Prisoner of Azkaban before s/he reads the Chamber of Secrets. 

Some kids want to read the A-Z Mysteries or 39 Clues in order, regardless of whether it makes a difference (and it doesn't).  But I'd love to have a way of knowing which series books must be read in order.  

                           These books have no visible numbers on the jackets.  

Which comes first? Does it matter?