Genre: If you have a bunch of different kinds of books, you might want to arrange them by genre. My own "library" is divided into the following sections: Fiction, Mystery, Reference, Art and Design Books, and Young Adult (I love Young Adult books. It's my dirty secret. Twilight was my gateway book.) Your library might include Graphic Novels, Science Fiction, Crocheting, Werewolves, or whatever it is you're interested in. Breaking things into genres can be tricky — why should Mystery be separate from Fiction, for example? — but as long as the categories make sense to you, the system will work.
Color: Now we're getting controversial. If you don't need to access particular books all the time, OR if you can easily identify your books by their spine color, then this could be for you. You can arrange them chromatically across a whole bookshelf or arrange them in color blocks. And you can have shelves where you alternate chunks of black and white so it looks like stripes. Lots of cool options for you! But again, you have to be okay not knowing where stuff is…
Color: Advanced Option #1: Arrange your books into patterns, like the American flag!
Color: Advanced Option #2: For the intrepid DIY-er, you can cover all of your books with kraft paper or other wrapping so they are all the same color. I would then recommend arranging them in some sort of order (and maybe labeling them neatly in white ink?) unless they really are just for show.
Chronological: For the nerds. This is how I arrange my art and design books, so the section starts with Ancient Greece, progresses to the Middle Ages, the Renaissance, the 18th century and then goes along by artistic movement (Art Nouveau, Wiener Werkstatte, Art Deco, Streamlining, etc.). I told you it was for the nerds.
Autobiographical: Remember in the movie "High Fidelity," how Rob (John Cusack) rearranges his records autobiographically, in the order that he discovered each one? You could do that with books. Caution: this probably only works if that's how your mind works. If someone says, The Great Gatsby, and you think, "junior year of high school!" Or if you think about Neruda's poems and immediately remember reading them during a particular relationship you had in 2003, then this could be a cool way to organize your books.
The Combo: This is a custom setting for those of us who aren't totally consistent. As I mentioned, I like to separate my books by genre. I like to arrange my fiction alphabetically by author's name. My non-fiction, however, I separate further into subject sub-sections, like Art & Design, Biography, Film Studies, etc., and then within those sub-headings I arrange them chronologically by subject.
Stacks: And though most of us arrange our books standing upright, stacks can be an aesthetically pleasing way to go (see image 8), especially for a smaller book collection. This method is physically better for the books, so it's something to consider seriously if you have any old or rare books.
How do you like to organize your books?