Obviously, if a reader likes a book they’re likely to want to read the next book in the series. Cover design within a series is all about making life easy for the reader – book 2 in the series should look as much like book 1 as possible. Another consideration is that series are usually stacked together on bookshelves, forming a large block ‘billboard’ of spines that can also be used to attract new readers.
With the Twilight series below, the covers all share the same design and together form an impressive large black colour block of spines.
A series with clever spine designs is the Mistborn Trilogy by Brandon Sanderson. On the spine, the ribbon connects to the next book in the series and the cover figure gets progressively closer.
I also have to mention a clever bit of cover design I've noticed for Brandon Sanderson's books. Since he became a bestseller, all his books have taken on similar design elements. They're all white with a single accent colour. Books within the same series (like the Mistborn Trilogy above) have the same accent colour. Books from different series have a different accent colour. See Elantris and The Way of Kings below. Both of these books are different series, but the standard design elements make it easy to find books by this author.
Update 22 June 2012:
I've also noticed another bit of cover trending here, with the Night Angel trilogy by Brent Weeks using similar design elements to Brandon Sanderson's for its covers. Brent Weeks and Brandon Sanderson target exactly the same demographic, so it makes sense for the covers to share design elements. If readers pick up a book by Brent Weeks when they wanted a book by Brandon Sanderson, it's a win from a marketing perspective because they have picked up a book they will probably be interested in anyway. I also wonder if it has anything to do with the fact that S and W are usually shelved fairly close together in the fantasy/sci-fi section of most bookstores.
Update 27 June 2012:
And yet more fantasy books to add to the trend pile! What is it with the ribbon love?