If you are using a Mac, and you want to copy your library, there is a program alled Migration assistant that makes things pretty easy. It’s located in your utilities folder (in the finder, click command shift u). Just open it and follow the instructions.
Alternatively, you could open itunes, select file/organize library/consolidate your library and after its finished file/organize library/ upgrade to iTunes media organization. This will take all of your music/movies/whatever on your computer and copy them to the itunes library folder (so obviously you’ll need at least twice as much free space as the size of the itunes collection on your HD to do this), and organize the files into artist/album folders. Once you’ve done that you can then simply drag and drop the itunes folder you just created onto an external drive, which you can then connect to the new computer and drag and drop the itunes folder you just created over the empty itunes folder on your new computer.
If however, you want to MOVE your media to a new mac (as opposed to copying the files) you could install a script on your computer called Groovy Moving (http://www.macupdate.com/info.php/id/24004) and then
start your new mac up in target disk mode (press power button while holding down “t” until the firewire icon appears), connect the computers with a firewire cable, open itunes, select all the songs in your library and run the script. whew. ok. Good Luck.