An online site for social networking around books is Book Sprouts. It is a free book club. You can join an existing club, start your own club and discuss the books you love. Book Sprouts lets you invite friends to join the book club (or clubs) that you are participating in. Book Sprout also offers suggestions for good books to read when you run out of ideas for your club.
Shelfari is a social network for people who want to share ideas about good books and see what other people are reading. At Shelfari you create a bookshelf showing what you are reading. If you have a blog, you can get a widget to show your bookshelf on your blog. You can also comment and review books on another member's bookshelf. Authors are featured with bios, videos and links to their own websites, which is a nice bonus. Shelfari is owned by Amazon.com.
Library Thing is a huge book club online with over 30 million books listed by members. Like Shelfari, Library Thing uses the bookshelf metaphor so that you can share the books you are reading and find others who are interested in discussing the same books.
Good Reads lets you look at others' collections, read and write reviews and share ideas. You can join a book group or a discussion. This site also provides a way for you to contact an author. A nice bonus for fans!