There are several search engines that allow users to search for a book by plot. One website is Whichbook.net, which allows users to search for a book based on their mood and the type of plot and themes they are looking for.
Whichbook is best for people who don't have a specific book in mind. For those who have a better idea of what they want to read, there is AllReaders.com. AllReaders allows searchers to input desired themes, plots and even writing style. Finally, there is LibraryThing.com. LibraryThing suggests books based on what the user has already read, as well as community reviews. The site also has an "Unsuggester," which lists books a reader probably won't like based on what they do like.