How can I do a Full Backup of my iTunes library (including Playlists and Album Art) to an external Hard Disk?
Luckily, Apple has heard your cries:
iTunes: Back up your iTunes library by copying to an external hard drive:


  Consolidate Library
  
  
  Open iTunes Preferences: 
  Choose iTunes > Preferences. 
  Click Advanced.
  Make sure the option to "Copy files to iTunes Media folder when adding to
  library" is selected.
  Click OK. 
  
  
  Note: After you click OK, iTunes
  copies any files that are added that
  weren't already in the iTunes Media
  folder and places the copies in the
  folder. The original files are left in
  their original locations. To save
  space on your hard disk, you might
  want to delete the original files
  after confirming import.
  
  
  Choose File > Library > Organize Library.
  Select the option to "Consolidate files."  
  
  
  Note: If you recently updated to
  iTunes 9, you might want to consider
  selecting the option to "Upgrade to
  iTunes Media organization." This
  updates the file organization of your
  iTunes Media folder.
  
  
  Click OK.
  
  
  Move to External Drive
  
  
  Quit iTunes.
  Locate your external hard drive. 
  On the desktop or Finder sidebar. 
  Locate your iTunes folder: 
  By default, the iTunes folder is located in: /Users/username/Music 
  
  
  If the iTunes folder is not in the
  default location listed above then you
  can find where the iTunes folder is
  located by following these
  instructions:
  
  
  Open your iTunes Preferences: 
  Choose iTunes > Preferences. 
  Click Advanced. The location of your iTunes folder will be listed in
  iTunes Media folder location box.
  Drag the iTunes folder to your external hard drive. This can take a
  while if you have a lot of items.
  When the transfer is complete, your iTunes Library will have been
  successfully copied to your external
  hard drive.
  
  
  Restoring your iTunes Library
  
  
  Quit iTunes.
  Locate your external hard drive. 
  On the Desktop or Finder sidebar. 
  Drag the iTunes folder (backed up earlier) from your external hard drive
  to whatever location you desire on
  your internal hard drive. It is
  recommended that you choose the
  default location for the iTunes
  folder, which is:
  /Users/username/Music 
  Open iTunes while holding down the Option key (Mac) or Shift key
  (Windows).
  In the resulting dialog, click the Choose Library button.