Unfortunately, LJBackup does not seem to work any more - you're welcome to try it if you'd like, but it will probably fail to login.
Want to move your LiveJournal to WordPress? See LJ to WordPress!
About this project: This project takes a LiveJournal and saves all the entries and comments, as well as calculating some interesting statistics. See a public-only backup of my LiveJournal. You might also be interested in LJBook, which will produce a nice-looking PDF document of your journal suitable for printing.
Source files (all of these were written in Ruby):