iTunes Backup

If you have checked the "Keep iTunes music folder organized" option in iTunes preferences -> Advanced, and have not moved the iTunes Music folder out of the iTunes folder in ~/Music/ then the easiest way is to drag and drop the whole iTunes folder over on the external drive.

If you manage the library yourself, then you might want to "Consolidate Library..." before moving it.


Edit: You may want to read some of Apple's Support articles, like Moving Your iTunes Music Folder and Backing up your music files in iTunes 4.

 

If you have an iPod you can use that as a backup of sorts. In the event that your computer dies, simply use one of the iPod utilities that are available, like the one in my signature, and it will recover your songs, playlists, play counts, last played, etc.