It is a good to routinely backup your iTunes playlists to an external drive or network drive, if you don't already have Time Machine running or a remote backup service. You might also want to use your playlists on another Mac. In any case, it is very easy to do this simple backup.
Open iTunes. Select the playlist you want to save. Click on File, Library, and choose Export Playlist.
Choose the XML format for easy compatibility. Name the backup file and Save.
You can repeat this process for all the other playlists that you want to backup.
Open iTunes on the machine with which you want to import your saved playlists.
Go to the File menu, and Library, and then choose Import Playlist. Select the XML files that you saved before.
Note, if you want to backup your entire iTunes library, which takes significantly longer, then you will have to make sure that you have the sufficient space to accommodate the size listed at the bottom of the main iTunes window. If you have enough space, you can go to the File menu, Library, and choose Back Up to Disc.