Every so often, I get calls from people about how to move or backup their iTunes libaries.  For the most part, backing up your collection to CD/DVD is probably the best.  And by backing up, I don't mean making audio CD's, but rather using the built in feature from iTunes to Back Up to Disc...  This lets you backup your entire iTunes library, or only iTunes Store purchases.  The later is the most critical thing for anyone that has purchased things from Apple iTunes.  I strongly recommend doing this often, since it should all fit on a very cheap CDR.

Once backed up you can take those CD/DVD's and restore your Library to another computer.  It keeps your playlists and media intact.

Another way, is to modify the libary files directly, which can be tricky.  But there is an article on Life Hacker that covers this.